You certainly could have incidents of US/UK & Soviet forces shooting at each other by accident. While this would piss everyone off, it would be tamped down quickly and acknowledged for the kind of error that happened. The USSR was exhausted, and still dependent in many ways on LL. The Uk was tapped out, and France was a mess. The USA was by no means exhausted. There was plenty of manpower, industrial capacity to spare and the USSR in 1945 and for some years thereafter had essentially no navy so getting stuff to Europe was easy - you'd probably have convoys because they would try to send a few subs out but basically it was a no-brainer. Poland could become a mess for the USSR, playing hob with logistics.
Having said all that, the UK was in no shape to do this and certainly the Labour Government would not do it, Stalin was going to get what he could by bluster but was in no shape to take on the W Allies. The USA, after defeating Japan had no reason to continue fighting now against the USSR. A serious conflict rather than some incidents needs to start on purpose, and nobody had the combination of ability to do so AND desire to so. One or the other perhaps but not both.