I have a rigid road bike right now, can I transform it into a full suspension mountain bike?
The simple answer is Daniel R Hicks' one: only by recycling the frame into a completely different shape.
Even trying to bolt on new parts for a half-way conversion will be difficult. The trivial difficulty is geometry. Road bikes usually have a high top tube and expect the rider to lean forward over the bars to improve aerodynamics. Mountain bikes are more upright to facilitate getting off the seat for bumps, and a low top tube to keep it away from your genitals.
More importantly, you will need disk brakes. If your road bike doesn't have them you will not have brakes after you convert it to a mountain bike. If you have disk brakes you could run 559 (26") wheels to get slightly fatter tyres, otherwise you'll be stuck with whatever you can fit into the frame (unlikely to be knobbly tyres). Slick tyres or no brakes, you decide... either way as soon as it gets a little muddy you're not going to have much control over the bike.
Suspension will be hard. You could probably fit a 29er MTB suspension fork to a road frame, which would also give you room for a fat tyre and front disk brakes. Doing so would almost certainly void the warranty, and the extra length would generate larger forces on the frame which may cause it to fail even if you only used it on the road.
Alternatively, Pantour make a front hub with ~12mm of suspension travel that you could build in to give you front suspension. Unfortunately their rear suspension seems not to have made it into production.
The only alternative I can think of is the "LoopWheels" but you would have to have disk brakes and be willing to fit very short cranks, as those wheels require a lot of space for movement (and are only available in 406 size). I suspect that you would have clearance for 100mm cranks at best, and then probably only after fitting a longer front fork.
So you could possibly do this, ending up with a frankenbike with a mountain bike front fork and wheel, short cranks and a 406 rear loopwheel. It would cost more than even a mid-range full suspension MTB and perform much, much worse until it inevitably broke. But it would be, in its own way, kind of cool.