this involves cheatmode and additional mod install, editing text files and reloading several times.
easiest way is just do Alt + ~ then type in the console config.cheat_mode 1 then open your inv in campaign map and give yourself the mortars, and find some engineers.

far more involved way:

Is your character a Vampire Count or other artillery quest locked culture? Heres how I made it work, with cheats and mods, but honestly I found the entire quest underwhelming so I was glad to be done with it quickly to access artillery:

- fresh start, 0 gunpowder skill Vampire Count console command your skill level to 50 or:
- go to Nuln, talk to the College Magister browse his scrolls/books and mouse over the effect of each book, theres several with gunpowder experience, best one is lock stock and barrel instant 30+ skill, then buy and use a gun till lvl 50 or buy several books and read all of them, after having bought it select the book in inventory and click the magnifying glass then wait in town for a about a day,
- once at 50 gunpowder skill, youre locked out of the quest! Empire of Men only! download and install the mod called Character Manager by Prozengan295,
- reload the game and go to the encyclopedia page of your character click save, this will create a document file save for your character,
- go to the save file and edit JUST your character's culture, NOT clan culture, change it to Empire of Men with the capitalization and spaces, just: Empire of Men
- save the file, back in the game click load on the encyclopedia page of your character, save the game and load the save file

DONE! your character can now start the quest. id reccommend doing ALT + ~ and typing in tor.whereisgoswin after starting the quest, because this quest is nonsense itll spawn a random party accross the world from your, just type the command and tp to it, kill the party then ALT + ~ again, type in config.cheat_mode 1 to enable cheats, then on the world map find Nuln again because the tor.whereisgoswin command teleported you 30 days away, so with cheats ON you can ctrl+click in front of nuln, walk in talk to engineer again and guess what HE HAS ANOTHER RANDOM PARTY for you to find! walk out and type tor.whereisgoswin again and it teleports you to second party accross the map you know the drill ctrl+click teleport back to Nuln turn in and finally finished the quest, BUT WAIT you cant buy artillery unless under the service of an imperial elector lord, at this point i gave up and just gave myself the cannons using cheat inventory, as I could at least hire engineers from the master engineer now.

now if you'd like to be a Vampire Count again, just edit the save file culture back to Vampire Count from Empire of Men, save and load ingame, then reload youre a Vampire with Artillery. Youre welcome :)