Best of ...
So first thing first, as for "best of Army" or "best of special forces", significant units portrayed in the movie are:
All of which are US Army units, all 3 are part of US Army Special Operations Command (USASOC). However only Delta and SOAR are classified as Tier One and are part of Joint Special Operations Command (JSOC), while Ranges are not. Thus arguably Delta, rather than Ranges could be considered "the very best of Army".
As for "the very best of special forces". I'm not going to do pointless exercise of without trying to argue if Delta is better that DEVGRU or vice-versa. There is CIA's Special Activities Division (SAD) which recruits the best of special Deltas, DEVGRU and STS 24th, of which the best are recruited for Special Operations Group (SOG) (source, mirrored here).
Now, in years prior to Battle of Mogadishu (1993) there where two significant conflicts in which US Army soldiers might have gotten combat experience.
Rangers, Deltas and SOAR all participated in the invasion of Panama. However that doesn't mean they've actually had contact with enemy, other than accepting their surrender.
The entire 75th Ranger Regiment participated in Operation Just Cause.
Rangers spearheaded the action by conducting two important operations.
Simultaneous parachute assaults were conducted onto Torrijos/Tocumen
International Airport, Rio Hato Airfield and General Manuel Noriega’s
beach house, to neutralize Panamanian Defense Forces. The Rangers
captured 1,014 Enemy Prisoners of War (EPW), and over 18,000 arms of
various types. (source)
Also in the entire operation Just Cause only 200-300 enemies were killed, while 27,684 U.S. troops and over 300 aircraft were used.
SOAR inserted Delta units inserted into Iraq for purpose designating Scuds during Scud hunting operation (source). This consisted primarily in staying undetected and laser-designating the targets, rather than firing small arms at the enemy. On rare occasion that did however occur:
The book, Delta, by Terry Griswold and D.M. Giangreco, describes a
Delta Force operation in which a team inserted by parachute into the
desert. Due to a shortage of helicopters, a small Delta Force team
performed a High Altitude High Opening (HAHO) jump from a USAF C-141b
Starlifter aircraft. Once on the ground, the unit set up a OP close to
a MSR. When they spotted a suspected SCUD convoy the Delta team called
in a series of air strikes by US and UK attack aircraft. Later, as the
Delta team attempted to covertly exfil the area, they bump into an
Iraqi foot patrol. A brief firefight ensued, resulting in one Delta
KIA and another with serious injuries. With extraction by helicopter
unavailable, a MC-130 was called in to carry our a surface-to-air
recovery (STAR) of the wounded trooper via the Fulton recovery system.
This goes ahead successfully and the rest of the unit are later
extracted by MH-60. (source)
Rangers participation in Desert Storm was very limited, their only deployment was to observation posts on Kuwait-Saudi Arabia border prior to ground assault. Their only combat experience was one of the observation posts being overrun in the battle of Khafji.
There were numerous Army infantry divisions participating, so it's possible that someone who later became Ranger or Delta had combat experience as regular grunt. However, unlike 2003 Invasion of Iraq and following occupation, Desert Storm was mostly fought on open desert, mostly by air assets and armor and mechanized infantry.
The definition of "combat experience"
There is assumption in the question, that combat experience means actually engaging enemy with direct fire weapons. In case of special forces such as Rangers or Deltas it's most often neither their mission nor even secondary objective. In fact more often avoiding detection is priority. Thus special forces which would infiltrate, carry out their mission and exfiltrate enemy territory w/o firing single shot from their weapons would still be considered to have gained combat experience.
Now vs then
The question is "Are many US Army Rangers young people with no combat experience?", however Battle of Mogadishu occurred in 1993. So past tense would be more appropriate. The answer above addresses implied question "In 1993, were many US Army Rangers young people with no combat experience?". What could have been the case in 1993 most likely is not be the case at all currently. For the last 12 years US has been engaged in one major war (Afghanistan) and for 9 of these years in another one (Iraq). 2.5 million soldiers have at one point in time been deployed to either of these war zones (source).