Is there a way to manually install Google Play store on a factory reset Xperia Play?

I factory reset my Sony Xperia Play because unfortunately it had become unusable. I factory reset it again and cleared the data after leaving the Market app to update itself didn't work. The Xperia Play is connected to wifi and I'm using an app password set via my Google account but the Market app crashes and a network error message pop-ups. Has anyone managed to get the Google Play store back after a factory reset? Edit: Android version 2.3.4