Well, if you want to go by the rule of "conceivably could have been recorded at home", there were "portable" VTRs being sold in 1963 (using 2" tape, written in a proprietary 2-head Ampex helical scan format). And for that matter, Hugh Hefner is reported to have had full-scale Ampex quad machines in the Mansion back in the 60s.
However, more likely to surface would be recordings in the open-reel 1/2" formats (similar to the UK Shibaden format), which first gained traction in the US market in about 1969. The "$10,000 Pyramid" episode opening with June Lockhart and Rob Reiner from 1973 is one of those. The oldest game show eps verified to exist in that format would be the reels in the UCLA archive that date from 1971, which happen to include (among other things) an episode from the opening week of the ABC version of "Password".
-Kevin