No you cannot get by with a single axle truck.
Why?
Because the way these trailers are designed is that the tongue transfers quite a bit of weight to the truck. So depending on how much weight is on the rear axle of a single axle truck you would probably be overloaded. And you don't want to move you load back on the trailer to lighten the tongue, because then it would tow squirrely and not very safe.
Also depending on where you are if you move the load back you will be overloaded on the trailer axles if it is a tandem. Around here we can carry 34,000 on a tandem, and 42,000 to 43,500 on a tri-axle depending on the spread. A tandem axle trailer 20 ton trailer weighs about 10,000 lbs., a tri-axle 25 ton trailer weighs about 13,000 lbs. And you are talking about carrying a 36,000 lb excavator. So if you figure this all out you need to transfer at least 10,000 and preferably more to the tongue for the truck to carry.
When I am hauling somthing this big on our TrailMax TRD50 tri-axle, I prefer about 15,000 lbs. on the tongue. It just seems to ride and tow better.
And as you can see this would probably overload a single axle, and I would want the extra brakes with a tandem.