Can I tell if I pregnant within 2-4 days after possible conception?

Not yet. Not with current technology. Though very close. Probably 5-6 days with the best of the over the counter tests. A blood test will be modestly sooner but not likely as early as 4-5 days. .
No. hCG (pregnancy hormone) is not detectable in blood or urine until at least 7 days after fertilization, because the amount of hCG is too low. We know that implantation cannot happen before 6-7 days, so embryo must be at LEAST that old before a test could detect. Some clinicians "define" implantation as when hCG can be detected, which would be more like 9-10-11 days. Good wishes.