The blood test is the earliest reliable option, it can detect low hCG levels before the urine kit does. But you still need to wait about a week to ten days after conception. Testing too soon can still miss it.
Not immediately after intercourse, but the blood beta hCG test can pick it up earlier than a urine kit, often around 8 to 10 days after conception. Its more sensitive than the home test. So it detects early, just not instantly.