Is there any way to manually install Google Play store in a factory reset of Xperia Play?

I rebooted my Sony Xperia Play from the factory because, unfortunately, it had become unusable. I could not restart it again and I deleted the data after leaving the Market application to update. The Xperia Play is connected to Wi-Fi and I am using an application password established through my Google account, but the Market application is blocked and an error message appears on the network. Has anyone managed to recover the Google Play store after a factory reset?