Is there any good evidence for or against this?
There are two HIV variants which stem from two different SIVs (Simian Immunodeficiency Virus):
The only species naturally infected with viruses closely related to HIV-2 is the sooty mangabey (Cercocebus atys) from western Africa, the region where HIV-2 is known to be endemic. Similarly, the only viruses very closely related to HIV-1 have been isolated from chimpanzees (Pan troglodytes), and in particular those from western equatorial Africa, again coinciding with the region that appears to be the hearth of the HIV-1 pandemic.
Ref: P M Sharp, E Bailes, R R Chaudhuri, C M Rodenburg, M O Santiago, and B H Hahn. The origins of acquired immune deficiency syndrome viruses: where and when?, Philos Trans R Soc Lond B Biol Sci. 2001 June 29; 356(1410): 867–876.
The abstract goes on to explain that several instances of Zoonosis have been observed in the genetic record of the virus going back before the 1940s when it was certainly not technologically possible to engineer a virus and mass vaccination of humans was not practiced in any case.
This article is where the team that found the (chimpanzee) source of HIV-1 published their findings, but does not include the full source. However, you can get it from the NIH here. And a summary from The Guardian here which mentions origins of HIV-1 dating back before the 1930s.
The more modern transmission events are addressed here:
Our research indicates that serial passage of partially adapted SIV between humans could produce the series of cumulative mutations sufficient for the emergence of epidemic HIV strains. We examined the rapid growth of unsterile injections in Africa beginning in the 1950s as a biologically plausible event capable of greatly increasing serial human passage of SIV and generating HIV by a series of multiple genetic transitions. We conclude that increased unsterile injecting in Africa during the period 1950–1970 provided the agent for SIV human infections to emerge as epidemic HIV in the modern era.
Full text is available from the NIH. By "increasing unsterile injections" they mean
80% of African households had experienced needle use in a two-week period by the 1960s (Birungi et al. 1994)