On what continent? An African upper palaeolithic site dated to 70,000 years ago is going to generate way more interest (and therefore more important scientists, more high tech equipment, much more funding, etc) than a European upper palaeolithic site dated to 35,000 years ago. (Due to historical racial bias, there's a ton of info already on Europe but a comparative lack of data in Africa and Asia, especially regarding our more recent evolutionary past, i.e. the last few hundred thousand years. Additionally, Africa is where most of human evolution took place so is naturally going to be where most of the important discoveries are made.)
What species of human? A 35,000 year old Neandertal site with upper palaeolithic tools and no evidence of Homo sapiens would generate a lot more interest than a 35,000 year old European Homo sapiens site with a typical array of upper palaoelithic tools. A previously unknown species of human (much more likely to be found in Asia or Africa) with upper palaeolithic tools would generate massive amounts of interest (scientists, technology, funding, etc) and the highest level of scientific study.
That doesn't mean that Homo sapiens sites from Europe 35,000 years ago or more recently aren't going to be considered important. They'd get at least the same level of care and scrutiny as, say, neolithic sites or Roman sites - more if there's anything new or special about the site. Trained people would be carefully excavating and cataloging everything that's found and there would be researchers studying what's found.
So the answer depends on all those things.
ETA: bear in mind that my frame of reference is from 7 million years ago to around 35,000 years ago and I'm talking comparative importance. All sites that ancient would be considered important. Just that there's a load of ways sites can be massively more important. Importance is relative to funding which means more people and more high tech equipment. There are devices that can be used to scan the ground and find what's buried in it before excavating anything. These have been used in various sites in Africa, e.g. sites with species dated to around 2-3 million years ago (emergence of the genus Homo) or around 4-7 million years ago (earliest hominins/when our lineage split from that of chimps). Most sites won't get the funding for that kind of thing. Bear this in mind in relation to my comments about importance.
ETA#2: there's a cave in Africa (I think the Rising Star cave system?) where they specifically recruited petite women for one part of the excavation as it required crawling into some tiny spaces. They would've had high tech equipment on such an excavation, and I think they already knew the stuff would be there. I don't have the details but it would be one to look into for your story research, as long as the importance of the find is relative to the amount of funding.