Let's see what we can find from reality, both present and historical. For reference with the dates in this post, the Bronze age lasted from very roughly 5,000 years ago to 3,000 years ago, though both start and end very much depend what region we're talking about.
The earliest bridges I can find:
Tello bridge is 4,000 years old, largest span ''unknown'', I couldn't find any cite, but seems largish given the humans in the picture. (via https://www.britishmuseum.org/blog/worlds-oldest-bridge-being-preserved-iraq) I'm not 100% convinced it was even a bridge.
Umshian root bridge is only maybe 130 years old, but suggests another possible method of creating a bridge if there are vines that have evolved to grow long and strong enough to go a long way down into the crevasse: just make the vines grow along ropes, and over time, grow it bigger. Admittedly, a rope bridge may be more practical! Not sure the span, but he seems to be 150ish pixels tall, but is leaning forwards, so may be foreshortened in this position; the bridge seems to be 1700pixels wide, so we can guess it's at least 12 m (40 ft) wide, and one source (https://morelifechanger.in/firming-double-decker-root-bridge/) claims it's "about 50 meters long" (~160 ft). (via https://en.wikipedia.org/wiki/Umshiang_Double-Decker_Root_Bridge)
The Tarr Steps are old (perhaps from the bronze age, others think medieval) but have very short spans, just a few feet each. It's also super unlikely that these are the original flags, given what feet and river floods will have done over the last few thousand years, so it's been rebuilt many times.
Arkadiko bridge has a TINY span. Just look at it. 1m (3 ft). And again, I'm a little skeptical of how original the stones are, but it's estimated about 3,000 years old. (via https://en.wikipedia.org/wiki/Arkadiko_Bridge)
The unfinished obelisk is not a bridge, but bear with me. This was a stone pillar, started about 3,500 years ago. It was planned to be the largest obelisk in Egypt. They stopped carving it when it cracked. BUT. It was 42 m long, and tapered. If it had worked, that'd make a nice big span!
If you have each side cooperating, and each one mines and pushes one of those out to the edge of the crevasse, you've got yourself a span that's about 40m of stone. More if you want to span the middle with a couple of trees. The danger is, of course, it's brittle, and likely to crack, and both sides are now near their tipping point and need counterweights. (via https://en.wikipedia.org/wiki/Unfinished_obelisk)
For comparison, Stonehenge's lintel stones (4,000 to 5,000 years old) are only 3 m (10 ft) long, and the unsupported length is even shorter. (via https://en.wikipedia.org/wiki/Stonehenge)
Convenient tall trees, or joined wood, would be better than stone. More flexible, lighter, easier to harvest, easier to counterweight, less prone to catastrophic cracking. Some of these, rarely, can grow to a height of over 100 m, making a bridge length of perhaps 80m entirely possible with both sides joining the trees. By binding a third tree tightly to join the two spans, you wouldn't even need to cantilever, at least not after construction. (via https://en.wikipedia.org/wiki/List_of_tallest_trees)
I still feel that the other answers are correct, though, and a rope bridge would be best, because at that point you're limited only by the strength and weight of the rope.
Queshuachaca bridge is at most one year old: it is normally remade annually, but collapsed in 2021 because it was not maintained in 2020. It was first built by the Incans about 650 years ago. Nobody knows when their practice of rope-bridge building started, though, other than that it goes back to at least Incan times. It has a span of 36 m (118 ft), but examples up to 45 m (147 ft) were once known. (via https://en.wikipedia.org/wiki/Queshuachaca)
Oh, here's one last idea: if the gorge is narrow enough, made of the right kind of rock, with the right faults, they could find a parallel faultline, and calve off a section to tip across and lean against the far side. Alternatively, they could try carving it out like the dolmen. Then once it's leaning against the other side, they can either carve steps in it, or just fill in the gap all the way up to ground level.