This answer assumes you have no interactions whatsoever with other Pokemon games. Interacting with other games to do things like trading something that knows surf might change the order you can get these. The answer is formatted as a list of events along with the baby Pokemon unlocked by each event.
Finish capture tutorial: Budew
Defeat Galactic grunts at Floaroma Meadow:
Munchlax might become obtainable as early as this, depending on your ID.
Defeat Mars at Valley Windworks: Cleffa, Chingling
Defeat Jupiter at Eterna City: Togepi
Visit Solaceon Town: Pichu
Defeat Cyrus at Celestic Town: Bonsly, Mime Jr., Azurill, Happiny, Magby
Munchlax might become obtainable as late as this, depending on your ID.
Finish Riley's side quest: Riolu
Talk to Professor Rowan after leaving Distortion World: Mantyke, Elekid
Upgrade to National Pokedex: Igglybuff, Tyrogue, Smoochum
Defeat champion: Wynaut