Well, I think it depends on what question we’re actually asking here. Is it theoretically possible - given only the info in the OT - that the Empire was much older than 20 years in ANH? Sure, it’s possible. There are many ways to write the backstory this way, as suggested in this thread, including but not limited to: (1) Vader was secretly evil for decades before giving birth to Luke, or (2) it wasn’t a secret and Mrs. Skywalker openly supported Vader’s murderous purge, or (3) there were other Jedi-killers before Vader, or (4) Luke and Leia were cryogenically frozen for some unspecified time period, etc. etc.

But none of those possibilities are the most straightforward, natural interpretation of the OT. The most natural interpretation is probably just the Empire was only 19 years old.

Or rather, with only ANH in mind, perhaps the Empire was substantially older. But with all three Original Trilogy films, the most natural conclusion is the Empire is the same age as Luke. Yes, it’s possible to come up with ways to extend the length, but they all involve “multiplying extra entities beyond necessity”, which makes William of Occam very sad.