After completing all of the AL, and all of the NL, available Missions in Conquest, two more Missions will unlock for you that require you to use the cards you've earned from Conquest to finish stat-based Missions which have to be completed in one match. Every one of those Missions will give you 5% progress towards the Conquest Program.
Once those Missions are completed, you'll unlock four more Missions. Two are stat-based Missions which need to be completed in a single game, and two Exchange Missions, one MLB The Show 19 participant Exchange, and 1 Souvenir Exchange. Total those, and you are going to be completed with Conquest Part One.
The Conquest Part One Program Reward is used to unlock Conquest Extreme, which rewards you for taking over strongholds in a particular amount of moves, culminating in tasking you with defeating all 30 strongholds in under 12 moves.
While performing those, and Advancing them in the Conquest Program, then you'll also be unlocking rewards and cards along the way. Defeating all of 30 strongholds will earn you a 10 Standard Bundle Bundle, additionally completing the 12 hidden MLB The Show 19 player Missions will bring you to a total of 60% completion in the Conquest Program.