Bone graft a month after tooth extraction instead of the same day?

I got tooth #3 extracted a month ago and have since learned it’s best to get a bone graft during the procedure. I’m supposed to get a bone graft in a week. Are there any major issues with this besides having to get two surgeries? Could the bone graft or implant be more likely to fail because I didn’t get the bone graft at the time of the extraction? I read a portion of jaw bone loss happens the first three months after extraction so it has me concerned.