Maybe start with extremophile cyanobacteria? That's what turned an ancient red earth into a blue one. It took multiple billions of years for them to produce enough O2 to make an atmosphere toxic to microorganisms that had evolved in the absence of it. But we're talking a *very* long term project here. Given it's about oxygen I could say "don't hold your breath".
Also, wasn't the issue with Biosphere II that they hadn't taken into account the O2 absorbtion properties of curing concrete (it takes a *lot*) or the shading from the structural (non transparent) parts of the dome? So more O2 being sucked up and not as much being produced (from less sunlight falling on plants). Either of those could cause problems, but both together meant they had no choice but to import O2.