I just bought car insurance yesterday and my car got vandalized the next day will the insurance company cover it

Your insurance should have an effective date. You are covered starting at the date and time stated by the policy.

Also, you must also have Comprehensive coverage for them to pay. This is the physical damage portion of the policy that pays for vandalism. If you have "Liability Only," the damage will not be covered.

Agreed if you bought it , when was it to be effective ? Often the day you pay for it, but not always, so that is the first issue, was a binder issued from the company.

Next was coverage for that paid for, also you may have a deductable you will pay first before they pay. My deductable for that is currently 500 dollars, but it depends on the coverage you bought