Can I have a health insurance that starts later than the date I land in USA with a J1 visa? [closed]

Potentially, yes. They may also not look at your documents. But it's a risk.

Note that (source):

If you are traveling to the US on a J1 or J2 visa, you will be required to carry medical health insurance for the full duration of your program. Many sponsor programs provide both their students and dependents with health insurance, or you will be required to enroll in a private health insurance plan. Either way, the US Department of State has minimum J1 health insurance requirements that your insurance plan must meet (which applies to J2 visa holders, as well).

Medical Benefits of at least $100,000 per accident or illness Repatriation of Remains in the amount of $25,000 Expenses associated with the medical evacuation of the exchange visitor to his or her home country in the amount of $50,000 A deductible not to exceed $500 per accident or illness A policy underwritten by an insurance carrier with: an A.M. Best rating of ‘‘A-’’ or above; a McGraw Hill Financial/Standard & Poor’s Claims paying Ability rating of ‘‘A-’’ or above; a Weiss Research, Inc. rating of ‘‘B+’’ or above; a Fitch Ratings, Inc. rating of ‘‘A-’’ or above; a Moody’s Investor Services rating of ‘‘A3’’ or above;