First of all, the first step in hypothesis testing is ... to have a hypothesis. You start with a "null hypothesis" that lays out some random process that the recorded data is hypothesized to have come from. Then the probability, given the null hypothesis, of seeing data as extreme or more extreme is calculated. If this is sufficiently small, then the null hypothesis is rejected. Saying "The probability of former Vice President Biden winning ... is less than one in a quadrillion" is not a valid statistical claim. It has to be worded as "The probability of former Vice President Biden winning given [null hypothesis] is less than one in a quadrillion". So we have to look at just what the null hypothesis is.
In the statement by Charles J. Cicchetti, Ph. D., we see:
The Georgia reversal in the outcome raises questions because the votes tabulated in the two time periods could not be random samples from the same population of all votes cast.
So this is the null hypothesis: the votes tabulated in the two time periods were random samples from the same population. In other words, suppose someone were to say:
Georgia's process of counting votes is to take all the votes, put them in a giant pile, thoroughly mix them together, and then randomly split them into one pile of votes that's counted on election day, and another pile that's counted after election day.
Cicchetti's analysis shows that the probability of seeing the results we saw, if that were in fact Georgia's vote-counting process, is less than one in a quadrillion. Cicchetti presented extremely strong evidence that the votes counted after election night had systemic differences from the votes counted on election night that are inconsistent with simply random chance (well, actually, he didn't actually present his calculations, and they probably aren't valid, since at this many standard deviation from the mean, normality probably is a problematic assumption, but I'm willing to accept that at least one calculation resulted in p < 10^-15). We can have very high confidence that the process outlined above is not how Georgia does things. Stated as I just did, this is a completely valid (albeit rather pointless) claim. Stated as "The probability of former Vice President Biden winning ... is less than one in a quadrillion", however, this is a misleading, if not outright dishonest, claim.
Having statistically proven that there was a systemic difference between the two sets of votes, the intent seems to be to imply that this difference was that the first set of votes was fair, and the second set was fraudulent. Cicchetti acknowledges that
I am aware of anecdotal statements from election night that some Democrat strongholds were yet to be tabulated. There was also some speculation that the yet-to-be counted ballots were absentee mail-in ballots. Either could cause the latter ballots to be non-randomly different than the nearly 95% of ballots counted by 3AM EST, but I am not aware of any actual data supporting that either of these events occurred. However, given the closeness of the vote in Georgia, 12,70 votes, further investigation and audits should be pursued before finalizing the outcome.
Now, that doesn't seem to be correct usage of "anecdotal". He seems to be just using a word with negative connotations to dismiss the claims, despite it not being applicable. If some "Democrat" (note that Joe Biden was the nominee of the Democratic Party, not the Democrat Party) strongholds were yet to be tabulated, that isn't an "anecdote", that's a well-documented fact. If ballots were mail-in, that again isn't "speculation", it's objectively verifiable.
Cicchetti's role is to provide "expert" (something I will touch on later) testimony on statistics. Whether or not he is "aware actual data supporting that either of these events occurred" is completely irrelevant, as he is not participating in this suit as an expert witness in Georgian politics (and he elsewhere mentions that he lives in California, which is about as far as one can get from Georgia, both geographically and politically), so what he is or is not "aware" of is not a proper subject of his statement, nor is what "further investigation and audits should be pursued".
This is an argument from ignorance: early votes were different from later votes, we don't know for sure that this wasn't due to fraud, so we should have an investigation to see whether it was. Cicchetti writes "These very different tabulations also suggest the strong need to determine why the outcome changed". First of all, again, Cicchetti is presented as an expert witness in statistics, not in electoral policy. Second ... really? Any time anyone has any curiosity regarding a statistical trend in electoral data, it's appropriate for them to file a lawsuit asking the courts to force the people running the election to explain it? The proper judicial response to this is "Cool story, bro".
Further, it's weird how these Republicans seem to take for granted that if the difference is due to fraud, it's fraud against them. Maybe the reason that the initial total favored Trump and the later one favored Biden was that the former was fraudulent and the latter was fair.
BTW, all these probabilities didn't all happen to come out to be the exact same number. The number quadrillion seems to be chosen simply as a number so large that getting a number any larger is unnecessary. Note the phrasing "less than one in a quadrillion"; this phrasing allows Cicchetti to avoid calculating an exact amount. But really, there's generally no need to calculate past one in a million; unless you're insisting that the probability of some systemic error that invalidates your statistical analysis is less than one in a million, reducing the probability from the statistical analysis to less than one in a million doesn't do anything for the overall probability. For instance, suppose a witness testifies that there's a one in a billion probability that some DNA didn't come from the defendant. If the probability that the DNA test was rigged is one in a million, then it doesn't matter whether the result of the test is "one in a billion" or "one in a quadrillion", the probability that the DNA isn't from the defendant is still at least one in a million.
There are further misleading claims in the statement, such as
Second, many Americans went to sleep election night with President Donald Trump (Trump) winning key battleground states, only to learn the next day that Biden surged ahead.
That is false. Trump never had a majority of the votes in those states. He had the majority of votes that had then been counted, but elections are won by having the majority of votes cast, not by having the majority of votes counted before midnight election night.
As for Cicchetti's suitability as an expert witness, he has no degree in statistics, and he repeatedly makes badly worded statements. He also says
The probability of there being no meaningful difference in voter preferences for Clinton and Biden would be approximately one divided by one with about a trillion zeros.
I don't know what he was thinking with that. To put this in perspective, suppose every Republican has a one in ten billion chance of voting for Biden. Then given a set of 100 million Republicans, the probability that all of them would vote for Biden would be one divided by a one followed by one billion zeros. Cicchetti is claiming that the probability of Biden outperforming Clinton by as much as he did by chance is one followed by one trillion zeros. 1/trillion is very different from 1/(10^trillion). The latter is just a ridiculous number.
Matt Parker's analysis: https://www.youtube.com/watch?v=ua5aOFi-DKs