Can you do a first response pregnancy test 2 days after intercourse?

No useful answer: Home pregnancy tests measure the urine level of the hormone hcg. Even if you have a fertilized ovum 2 days after intercourse the embryo will not have implanted and grown enough of a placenta to make HCG in measurable quantities. So you could do the test but the negative result you would get wouldn't tell you anything about the outcome of the intercourse 2 days earlier.

Too early: First response early result pregnancy test is reported to detect pregnancy up to 6 days before your missed period. Two days is just way too early.