I'm wondering how long will it take for my extraction gaps to close?

Weeks to months: I'm sorry for this vague answer, but your expectation of "gaps to close" is hard to gauge. Wound closure--bone is no longer exposed, and gum is covering and sealing off the bone--will be and should be quick. This till take a week or a little more. For the crater-like dent to disappear completely, you may be waiting for months. Your systemic health also matters. Unhealthy body is slow to heal.