Is it possible to set a release date on the google play store?

This is now possible using timed publishing. It appears to be restricted to updates so it may not work for the initial launch unless the app is published to your alpha or beta channels first.

In the new Google Play Console, You could use managed publishing

You can use managed publishing to control exactly when changes to your app are published. When managed publishing is turned on, you can clearly see which changes you submit are in review and which changes are ready for publishing on the Publishing overview page.

1- go to Publishing overview 2- click on manage, then turn it on.