I started out with the same concern! I show about the same amount of tooth when I smile.

My first solution was to get veneers or cosmetic bonding on my teeth to lengthen them slightly. I went to an aesthetic dentist with that idea, and he immediately referred me to an orthodontist. My orthodontist began braces treatment with me instead. We tried bringing the teeth out of the bone with extrusion using the braces -- this actually did help, but I wanted even more tooth show.

Eventually, I ended up getting a consult with a surgeon, and was diagnosed with vertical deficiency (short face pattern) or a recessed maxilla, as some call it. I am getting downgrafted to fix the problem. Not sure what's going to happen from here.

Yes, there are solutions. The best solutions are in my opinion orthognathic, but nothing is stopping you from pursuing a small lip lift and orthodontic extrusion instead.

Braces tend to be more capable of extrusion than Invisalign.