The stimulus check represented 804 billion dollars in direct to citizen spending of the government's 6 trillion dollars in spending. If your argument is "giving money directly to individuals causes inflation" we can start there, but government spending alone does not cause inflation; the Emergency Economic Stabilization Act did not meaningfully grow inflation.
We probably would not know fully in 5-10 years, but my own hypothesis is that America had it's own dark labor pool of incredibly cheap labor and when (1) Citizens were allowed to have some breathing room and look for better oppurtunities and (2) the CBP used Covid to massively ramp up deportations, labor became more expensive which clearly affected the rest of the economy.