I tested the oldest that would run at all for me. But I know that prior to 0.8 that you will have to do something about the BDB locks situation,
I also know that the BDB locks fix shared around back in 2013 will only take you up to 2016 or 2017 or something and then it still runs out of BDB locks.
Both Jameson Lopp and I have attempted syncing older versions recently:
https://blog.lopp.net/running-bitcoin-core-v0-7-and-earlier/ and
https://achow101.com/2022/03/syncing-0.5.0.
Without BDB locks configuring, 0.3.20 gets to block 124,275, 0.4 and 0.4 to 258,354, and 0.6 and 0.7 to 364,670. With a high enough BDB locks settings, I was able to get 0.5 to tip after 2 weeks of syncing. I didn't try anything older all the way because I didn't have the patience to wait that long.