Genie+ and Individual Lightning Lanes do refill throughout the day. In fact, Genie+ attractions often add extra "reservation slots" between 7:05 and 7:30 AM, and Individual Lightning Lane attractions likewise add slots at 1PM.
There are proven "power user" strategies that can improve your chances of getting the reservations you want as soon as they become available at 7AM. If you're interested, do a quick search for related articles on Disney Tourist Blog or Touringplans.com, or check Touring Plans' YouTube channel.
One last tip, if you weren't aware (I mention it because of how someone worded their reply) ... you do not have to physically be in the parks at 7AM to use Genie+. You can be at the park, at a Disney resort, off property, pretty much anywhere.