Rivnuts from Homestead, PA on 6/14/2020 4:53:31 PM:
Downtown parking is a function of how long you need to park. If you are literally just being dropped off without the need to park per se', you can likely do so on Commonwealth Place across from the Wyndham Grand Hotel at the entrance to Point State Park. If you need to park a little longer you can probably find paid meter parking on the Boulevard of the Allies also near the entrance to Point State Park. If you need to park for hours, there are a couple of parking garages on Ft. Duquesne Boulevard. See the satellite view of the area on Google Maps to get a better idea where these streets and garages are.
If you are staying in or around downtown Pittsburgh the night before departing on your trip, you can likely ride your bike to Point State Park without having to be dropped off e.g. along the Three Rivers Heritage Trail, Eliza Furnace Trail, or others. The website below provides a good map of those downtown trails.
https://friendsoftheriverfront.org/wp-content/uploads/2019/07/FotR_SouthSideMap.pdf
Since I live and ride along the GAP Trail to and around downtown Pittsburgh regularly, I'd be more than happy to meet you and guide you into, around and out of town. Pittsburgh can be a minor challenge to get around and out of town, but you'll find lots of riders along the trails that would be more than willing to provide assistance.
Lastly, if you truly want to start at the literal "Point" make sure you ride along the lower level pathway around the Point and its fountain and get a picture of the 4-ft diameter medallion embedded in the pathway that marks the convergence of the Allegheny and Monongahela Rivers that form the Ohio River.
Feel free to ask any further questions about Pittsburgh or the trails that may arise.