Reconstruct aggragate state from given point in time using CQRS and Event Sourcing

Let's assume I would like to get aggregate projection from a given point in time and I use CQRS and Event Sourcing based architecture.

Moreover, I have both read and write database. First one is powered by events and there are some aggregate projections to utilize by UI.

My question is - what is the best approach to reconstruct aggregate state from a given point in time in such an architecture, and briefly how it should look from an architectural point of view.

Note: I want to return such a projection to the client side.