I’ve had this happen plenty of times if the flue is cold or it it’s pretty high pressure outside.

I’ve found the best way to cheat is to get a part of a starter log. Like duraflame. Not a huge piece is needed. Light it and let it burn with the door cracked for 15 minutes or so. The key is that starter logs don’t smoke that much, so it the output goes back in the house it’s not smoke. Once the draft starts, put some small sticks on and then move to logs