Tech tree says 'gunpowder discovered c.1260'.

As we all know, they really mean the skill of making it finally leaks as far as Europe, having originated in China.

Minimum of Keep level in order to build gunsmith, then workshop, guild, master in successive castle levels upwards of that.

Minimum of Castle to build the Bell Foundry, which evolves into the Cannon Foundry in Citadel, Fortress.

If tight on funds, you'll likely end up building the cannon tech in the province with your most advanced fortification and ship-building facility combined, so you can get to ships with cannons but then finding long ship training times competing with your need for field cannon, so aim for at least two Citadels, one with a dockyard, in time for the arrival of gunpowder tech.

Gunner training centres could be placed just about anywhere at keep level, so as not to end up competing for building/training time.