Rent a wet and dry sofa/carpet vacuum, like a Kärcher Puzzi (I know). I did recently for my sofa - a good machine will cost 1500 or so, but I only paid 30 to rent it for a day.

They’re dead easy to use and you’ll be shocked at the amount of grime that comes out.

Baking soda, vinegar, and and all those other house-wife hacks are bullshit and won’t help you at all.

As an aside; baking soda and vinegar does fuck all. They break down to salt water. There is no cleaning magic happening. You can use baking soda or vinegar depending on what you clean, but most certainly not on a mattress that requires deep cleaning.

Finally invest in a protector and possibly a waterproof pad in between. The protectors are washable, so chuck that in the washer every so often and you’re golden.