If alternative suppliers arent possible, why arent they charging more already?

In the context of blanket import tariffs, the alternative to foreign suppliers are domestic suppliers, and it does already happen. For example, produce prices fluctuate depending on whether the produce is "in season" or not. If something can't be sourced locally or the local supply is reduced, the grocery store charges you more for it because of the additional costs in sourcing it from elsewhere.

Food aside, adding tariffs to everything imported is intended to disincentivize importing goods over domestic production. When demand exceeds domestic supply (and it will*), importing is still going to be necessary to meet that demand. This happens all throughout the supply chain, too. The only difference between now and then is that right now the consumer isn't paying a bonus fee for those imported goods or the imported raw materials used to create them.

*There is not a single industrialized country that is entirely self-sufficient and without imports.