Is it possible solutions for crowded teeth instead of premolar extractions?

Ortho: Without early phase ortho there can be insufficient space to open crowded teeth and extractions may be needed. Extractions would be more conservative than surgery and I am not sure to what extent some of the newer pins, etc can aid in that, they work with intrusion well. See a qualified orthodontist for all your options. If very crowded and bite issues restorations may not be an option.

Orthodontic consult: I'm not sure if an orthodontist already told you that you need some teeth removed, or if it is just your assumption. Not all cases of crowding require removal of teeth. Also, not removing teeth when it is advisable may leave you with a less than ideal outcome. Speak to an orthodontist, or even 2 or 3 until you find one you trust and his\her treatment plan aligns with your wishes and expectations.

Size of container: Cant put 2 quarts int a 1 quart container. 30% of all orthodontic patients have too much tooth material for the amount of bone they have in their jaws. If such a discrepancy exists, extractions mandatory. If enough bone support exists, rx can be done without extractions. See a qualified orthodontic specialist who does nothing but orthodontic treatment.