Reading your guys posts I think you are missing the meaning of this
させていただく or させてもらう is just less direct way of say you’re going to do something (usually in a situation involving someone else). It’s a set phrase if anything at this point
始めさせていただきます is just “I’ll start” meaning wise.
Is I’ll first start with a question(s) for the parents. (Polite)
Causative+もらう is a very common pattern so I highly recommend commiting this to memory and thinking of it as a package deal.