You are entering to a grandfather paradox. So, Sator's plan was to blow the Algorithm in the past. We know that SOMETHING DOES blow up there because Michael Caine's character (of the same name) mentioned about the explosion that occured. So that timeline is already fixed. They cannot recreate the past, but they were already predestined for the things in the past to already happened. Sator from hearing about the explosion at his home town ASSUMED the device worked which set motion for him to do what he thought would be his success. But he was mistaken and fooled bu the TENET organization to make it appear the algorithm exploded. Sator's fatal flaw was thinking by setting it up in the PAST would work, because he did not fathom the grandfather paradox of "what happens, happened". Had Sator collected the Algorithm and motioned it to sometime in the future, he MAY have a chance, but being that the protagonist is technically FROM the future and created TENET, Sator would of had to outlive the protagonist to be that far out into the future, and he was already dying of cancer so it was moot at any point, because he was technically the past in the future protagonist's eyes. What's destined is destined no matter.
But to get your your question directly. Team TENET knew that Sator would know they were going to search for the Algorithm. They even figured that he'll have something up his sleeve for precaution, which he DID. Had it only been the forward moving RED TEAM that the protagonist was on, they would of went into that same booby-trap, Sator would of had his goon that was waiting to set off the Algorithm to shoot the protagonist and Ives in the head like we saw in the film, the ONLY difference is there WOULDN'T BE an inverted NEIL to save their lives taking that bullet for them. You see, the plan was just to stated, to go there to dig it back up and destroying it, but the catch was Sator expecting them to come, which is why they did the "temporal princer movement" where one team goes forward and the other inverted within the ten minute span. They were expecting the inverted team to catch anything Sator was trying to do. Neil, being on the blue inverted team saw the booby-trap but it was too late, so he went in another opening to warn them about the trap. It wasn't that simple as to just waltz up in there. And everything was already predestined so things that happened MEANT to happen that way no matter what.