Short answer: No. The original The Sims (2000) launched exclusively on PC and Mac. It never received a PlayStation Portable port.
No version of The Sims 1, The Sims 3, or The Sims 4 ever arrived on the PSP. For handheld Sims today, your best bets are The Sims 4 via Steam Deck, Nintendo Switch (cloud streaming), or the mobile titles The Sims FreePlay and The Sims Mobile.