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The first five generations of game consoles typically had no backward compatibility. New console, new hardware design, new games. (An exception was the Atari 7800, which as far as I know was the first console to have backward compatibility. Conjecture: this was because it was released in the aftermath of Atari's dramatic fall from leading position, creating a very strong incentive to try to recapture what they had.)

The PlayStation 2 famously had backward compatibility, essentially by incorporating a PS1 onto a chip (and of course taking advantage of the ability of a DVD drive to read CDs).

But subsequent consoles such as the PlayStation 3 and Nintendo Wii began a strange pattern: initial backward compatibility subsequently dropped in a cost-reduced model. I can understand the desire to reduce cost by cutting features, and that backward compatibility is less important as a console builds up its own catalog, but I would also have expected the cost of continuing to provide it to keep dropping. (If it's just one cheap chip, might as well keep it.)

Conjecture: By the seventh generation, silicon process technology was not improving as rapidly as it had, so the cost of continuing to provide backward compatibility stayed nontrivial.

Alternative conjecture: Moore's law was still running fine, and the real reason for dropping compatibility was to encourage people to buy new games, which is where the profit in the console business comes from.

The first conjecture would predict temporary backward compatibility began with the seventh generation. The second would predict it could happen in any generation (except where there was something like a medium change from cartridge to disk).

So:

What was the first console to have temporary backward compatibility? Did it happen before the seventh generation?

The Mega Drive 1 and 2 can run Master System software via the Powerbase Converter. Neither the Nomad (the portable Mega Drive) nor the Mega Drive 3 are capable of doing so without further internal modification.

I therefore posit the Mega Drive.

The Mega Drive/Genesis is the obvious answer, but I can also make a case for the earlier Master System. Initial models were fully compatible with Sega's prior console, the somewhat obscure SG-1000. However, with the removal of the card slot and expansion port in later revisions this was severely eroded. Some games on cartridges may still work, but anything on a card or that requires a peripheral will definitely leave you out of luck. It has to be said that there weren't a lot of SG-1000 games seen in the West in the first place though.

What I'd suspect it comes down to is that backwards compatibility is of high utility on new consoles. Their games library is small and there's a lot of extra utility in enabling the machines to access the software for their immediate predecessors. However, as time goes by this utility is eroded, and any extra hardware required to support them becomes dead weight. If removing it offers any potential for a price drop, that's inevitably going to happen at some point.