Leaving before the crack of dawn is not going to help you. Dawn comes mighty early in Costa Rica but the gates at Poas do not open until 8 AM.
LaPaz Waterfall Gardens typically takes 2-3 hours minimum to explore. If you want to just hike along the river and see the waterfalls that will be a very expensive hike. You can see the best of the waterfalls and walk behind LaPaz waterfall without paying to enter the Waterfall Gardens. Just past the entry and down the hill, the road takes a hairpin turn to cross the runout from the main LaPaz waterfall and its a freebie worth stopping to see.
There are waterfalls and there are short hikes in Braullio Carrillo but you won't find a waterfall on one of the short hikes accessible from Hwy 32 near the ranger stations. Don't try hiking Barva without a guide. The short trails near the Zurqui and Quebrada Gonzalez Ranger Stations are easily accessible from the highway. Trails are often muddy and don't leave anything of value in your parked car as there have been thefts in this area. Found this description of the trails online (It was too muddy to hike the last time we stopped at the ranger station):
You'll find two main hiking trails at Zurqui Ranger Station. The Capulin Loop Trail, located across the road from the station, will take you through primary and secondary forest. The Natural Botarama Trail, located at the Carillo Ranger Station (Quebrada Gonzalez), 9 miles northeast of Zurqui, leads you on a two mile walk through primary and secondary forest.
Be sure and take roadadvisor's warnings seriously as these are not tame little nature trails and frankly I think it would be foolish to hike them all by yourself.