You can put raw sausage on a pizza, and in most pizzerias that is exactly how it is done. Bulk Italian-style pork sausage gets pinched into small nuggets straight from the tray and scattered over the cheese, where it cooks in the oven and drips seasoned fat into everything around it. The catch is size. A nugget the width of your thumbnail will be done long before the crust is; a thick slice off a link will not.
Everything else about raw sausage on pizza follows from that one constraint.
The temperature the pieces have to reach
Sausage is ground meat, and ground meat needs a higher internal temperature than a whole cut. Surface bacteria on an intact muscle stay on the surface; grinding folds that surface through the whole mass. The standard food-safety target for ground pork and beef is 70 °C (158 °F) held briefly, though slightly lower temperatures work when held longer: 63 °C (145 °F) for three minutes, or 65 °C (150 °F) for one minute, achieves the same reduction. Ground poultry goes higher, to 74 °C (165 °F).
That last line is the one people miss. Chicken and turkey sausage sit in a higher bracket than pork, which is a good argument for cooking those before they go anywhere near dough.
A pizza oven is easily hot enough to get there, but only if the heat can reach the middle of every piece. Size is the variable you control, and it matters more for sausage than for any other raw topping on a pizza. A nugget that is 15 mm (5/8 in) across and flattened slightly will reach 70 °C (158 °F) in the centre well within the time a home oven takes to bake a pizza. A nugget twice that size may not, because the outer layer insulates the core with rendered fat once it starts cooking. The temperature difference between pork and poultry sausage also matters more than most home cooks realise, and that difference alone is a good reason to treat chicken and turkey sausage differently on a pizza.
Fat and the size of the piece
Fresh sausage carries far more fat than most people picture. A raw Italian-style pork sausage runs around a quarter fat by weight, and some coarser-ground varieties push past that. Leaner fresh sausages carry noticeably less.
High fat content is a gift on a pizza. It renders during the bake, carries fennel and chilli and garlic across the surface of the pie, and seasons the cheese in a way a pre-cooked crumble never manages. It is also why the pieces have to be small. Fat renders outward from the surface, so a large lump insulates its own centre with a layer of rendering fat while the outside browns.
Pinch pieces roughly the size of a hazelnut, about 15 mm (5/8 in) across, and press them slightly flat as you place them. Flat is better than round for the same weight, because the heat has less distance to travel. Space them out so no two pieces touch, and put them on top of the cheese, never under it, where a blanket of mozzarella would shield them from the direct heat they need.
Bulk sausage against links and crumbles
Bulk sausage, sold loose in a tray or a chub, is the raw format built for this. No casing, easy to portion, and the texture stays tender because you never cooked it twice.
Links are a different problem. The casing does not render and does not soften in a pizza bake, so it stays chewy and separates from the meat. Slit the casing and squeeze the filling out, then treat it as bulk. Slicing a raw link into coins and laying them on the pie gives you thick discs with casing around the edge, which is the worst of both.
Pre-cooked sausage crumbles are the safe option and the least interesting one. The meat has already lost its fat and juice, so the pizza gets none of the basting.
Chicken and turkey sausage should be cooked first almost every time. They are lean, they dry out fast, and they have a higher temperature to reach.
Ovens that change the answer
A home oven at its maximum, around 250 °C (480 °F), with a stone or steel gives a bake long enough that small raw nuggets come out perfectly. This is the standard case, and it is why raw sausage is the default in most home recipes.
A very hot pizza oven, 400 °C (750 °F) or above, that finishes a pie in a minute and a half is a different situation. The crust is done before the interior of anything sitting on top of it, and sausage nuggets that survive that bake have to be tiny. Many people running one of those ovens brown their sausage lightly on a pan first, then finish it on the pizza, which gives the colour and the safety margin without cooking out the fat.
Deep dish and pan pizza go the other way. Long bakes, thick cheese layers, and often a layer of sausage pressed flat like a patty. Raw works well there, though the sausage sits under cheese and sauce, so the bake needs the time.
The pizza to try it on
Fennel sausage on a red pie is the version to start with, because the fennel seed blooms in the rendering fat and perfumes the whole pizza. Italian sausage with fennel is the pairing that made this topping a classic, and it needs nothing else except good mozzarella and a thin scrape of sauce.
If you want the sausage to be the centrepiece of the whole pie, the meatball sub pizza approach works: bigger pinched portions with ricotta between them, on a crust sturdy enough to hold the fat.
Build one tonight. Take bulk fennel sausage out of the fridge cold, pinch it into hazelnut-sized pieces with wet fingers so it does not stick, flatten each one slightly, scatter them over the cheese with gaps between, and bake as hot as the oven goes. When the pie comes out, cut into one piece before you slice. If the centre is still pink, you made them too big, and the fix next time is smaller pieces rather than a longer bake that would ruin the crust.