Spam-risk and shoulder work ahead

Synagogues weren't "authorized" by God. Sometime in the days when Israel was in or just getting out of exile with Babylon, it developed - probably as a means of encouraging one another while they were "away from home". They weren't allowed to offer sacrifices outside of the temple worship system and especially not outside of Jerusalem, so at some point synagogues came into existence - first as a gathering and then as formal locations with buildings called "synagogues". If you read through the Old Testament, they're not mentioned at all. It's only when you get to the gospels you run into them being mentioned. Something developed to replace their temple worship, per se, after Solomon's Temple was destroyed. And even after a new version of the temple was built, they continued on with synagogues in their various locations. God didn't say "make synagogues" but they did. There's no indication they were condemned by God ...