Many animals begin tool-making without free limbs. Dolphins use found objects (including sponges and shells) held in their mouth to scrape the ocean bottom (in relatively shallow waters) disturbing burrowing creatures that jump up; then they drop their tool and eat them.
A mahout (elephant handler) working with his animal to clear out dead forest trees reports that after pushing down one tree, a branch fell on the elephant's back; almost striking him (the mahout) too. Without prompting, the elephant stopped, tore branches from another tree, and propped the log between its trunk and tusks; extending well above its head and across its back. The elephant carried the log with it to new trees, deflecting many dead branches during the day.
Corvids (Crows, other large birds in the family) routinely construct many varied tools using only their beak and feet. They also seem to understand some of the tools of humans: One ice fisher (human) had a particular ice hole that he never caught any fish in, even when his other holes were producing a few fish every day. He set up a camera to film the hole; and sure enough, after some hours of film he saw the line moving. So, apparently, did a crow, because within minutes it landed near the hole; grabbed the line with its feet and began pulling away, flapping its wings; and eventually pulled a fish out. Not only that, but the crow spend several minutes after the fish expired extracting the hook from its mouth; and when it finally did that, put the hook and line back in the hole. Perhaps to catch another fish, or perhaps to conceal its presence (Corvids are known to engage in deceptive and cover-up behaviors with their own kind).
One of my cats, as a kitten, would spend many minutes on its back, even falling asleep that way, batting at tassles on the kitchen curtains with its front paws. Your animals, if they need both hands to fashion something, could do the same: Don't get hung up on the human posture of crouching over something and working on it; that is just body-mechanics for us.
If they do something, they will use their own body mechanics; I can easily see them doing something on their back, in the air, like braiding hair into rope, weaving, carving wood with flint, etc. For operations requiring a "gravity assist" so pieces fall away; just move the arms to the side. Or, they could obviously stand up like my dog or cat; so give them a table chest-high in the standing position so they can rest their elbows on it and manipulate something on it. The same goes for their sitting position; they can sit and prop their front elbows on a platform.
Note they do not have to build a table to discover this is a comfortable position for, say, knapping flint: Just encounter a natural flat rock of the correct height; and then reproduce that idea with found rocks; or logs, or cut a section of tree trunk so the length is the right height, carved pretty flat on both ends; then turn it 90 degrees. You have a flat round table. Slightly higher tech in the next few hundred years and they will be building tables from lumber; using the Mortise and Tenon method with animal-derived glues, as humans have been doing for at least 7000 years, and 4000 years before the iron age.
They can find body positions, slings, tables and chairs to free up their front legs and hands. Birds can stand on one foot and use the other to hold things they are constructing with their beak, like a termite spear.
It is misguided foolishness to think opposable thumbs are needed (dolphins, octopi and elephants don't need them, crows build a few tools using only their beak), or to think that free limbs must be always free. What is needed is intelligence and self-awareness, once those exists the animal will find a way to use its body to turn objects into tools.
added: Watching my cat; he sometimes lies on the floor and plays with a toy using both his front paws and his mouth; his furry elbows slide easily on the smooth wood floor with no trouble.
Also, I note that I sit most of my work day in a chair that actually holds my body in a comfortable position I couldn't possibly hold for more than a few seconds without the chair; thus an unnatural position without a support mechanism. Trying to think similarly for a cat-like creature; all that is needed is to remove the need for the front arms to support the body: The "chair" for that would be something like a bench it could rest its chest upon, that supported its body. Perhaps most of it; like our chairs support all of our weight but leave our feet touching the ground (for most).
A more sophisticated and comfortable version of that for your creature would be an angled bench-like padded cradle; supporting about from the armpit area back to the bottom of the rib-cage, high enough to support almost all the body weight and leave the back haunches in a natural crouch position; and leaving their belly and genitalia uncompressed. The support would allow them the free use of their arms, hands, and head: They could assemble things, write, look through microscopes, and do anything we do in chairs.
Like our own furniture; the cat chair would be low enough so that if they just stood up they would clear it by a few inches so could back away from it; it would be as easy for them to get into and out of as our own chairs.