Exact treatment depends on the cause of gap. Grossly there are many options- and Orthodontic treatment is least invasive.. No damage,no crowns. If you are concerned about the metallic appearance of braces then you could probably think of lingual braces (One from inner side of teeth) or you could opt for thermoplastic aligners(most Orthodontists are trained to do treatment with aligners). Meet your nearest orthodontist for more details

The gap in relation to the upper teeth seems to be very wide, best long-term option woud be crowns preferably all ceramic with high esthetic quotient index in mind. But clinical examination of the gaps and bite between upper and lower with enough space clearance would suffice better treatment options.

The best treatment would be braces but as u don't want clips u are left with only option of crowns