Dan, my friend and brother. Loved your previous message! Wow. Amen.
Back to your original inquiry regarding the origins of the synagogue.
The first Christians came over from the Jewish community. They already had a long history of regular public meetings for instruction and fellowship. They were now born again and eager to be with their new spiritual family. Personally, I would say that they were ready to tear the door off the hinges to get to these meetings.
The synagogue was the center of the community and a joyful place, too. There they would see their relatives and friends and also make new ones. There they would learn news things - as the truth was told and the scrolls unrolled. There they would get the latest news often passed around as prayer requests. :) There they would receive a holy kiss or perhaps have their feet washed. Since the meeting was open, things were a little unpredictable. Especially with regard to who might show up to speak.
As John wrote: We know that we have passed out of death into life because we love the brothers. 1 John 3:14. What could be more intuitive and natural than to be with those whom you love?
We do however notice a warning about failing to meet with others. It's found in Hebrews and you are familiar with it. And familiar with those who translate it to mean something else. "Don't go to church - just be the church". The greek verb here for meeting surely refers to synagogue: epiSunagoge. On that we can agree. Just as the word for church is a general word also meaning an assembly of persons for a specific purpose.
In summary, although there is no direct NT command to meet, there is one which forbids not meeting - failing to assemble. Which is really... the same idea.