This question is based on three assumptions (which I assume to be true - please correct me if I'm wrong):
- You can only obtain Mew by purchasing a Pokeball Plus, which contains exactly one Mew
- You can't breed Pokemon in the Let's Go games
- You can't transfer any Pokemon that didn't already come from another Let's Go game to a Let's Go game through Pokemon Home
Considering all of that, it seems to me that the number of Mews in Let's Go world-wide is finite. So if you only pick up the game now and are missing the Pokeball Plus, are you unable to complete the Pokedex unless you happen to meet someone by chance who is willing to trade you their Mew?
TL;DR: Is Mew required to complete the Pokedex in Let's Go Pikachu/Eevee?