Both are possible.

You can have alternative app stores on Android without any restrictions — the most famous example would be F-Droid which hosts free software. Nothing stops Epic, Meta or any company from also having such a store.

When you ship a certified Android, it has to come pre-installed with the Google Play Store but some vendors like Amazon and Huawei ship an alternative OS with their own stores to replace the Google one. It's not officially Android but can be based on the Android Open Source Project.

Very few companies have chosen to do either and it was usually because they were forced to (Huawei).