Just read an interesting Master's thesis from 2016. The topic was "Procurement principles and vendor management in technological start-up companies".

I'll just add a quote here:

"The interviewed start-up companies declared that their biggest challenges regarding their direct procurement activities were payment terms, delivery times, minimum order quantities, pricing and finding the right partner (Immonen, 2016)."

The above functions are something that is typically agreed upon in contract negotiations. I know startups typically use supplier's contracts or they go for the relational contract (ie. verbal) probably to save time. But it might be possible to have a quick checklist on the procurement side of things, too.

How big does a startup need to grow before these areas are set under the scope?