Please accept my sympathies on the loss of your dad. God bless him and your family.
There is no one place to check to see if life insurance was in effect at the time of one's passing.
All you can do is look your dad's belongings and papers. If you find evidence of life insurance, check with the companies directly. You can also check his paid checks or banking records and see if he was paying any premiums regularly by check or online payment.
Social security pays a small death benefit. It amounts to $255. It's small, but it'll help a bit. Contact SS to determine how to get the payment.
If he was a veteran, local veterans groups will help with some of the costs, sometimes. Ask, you never know.
All vets can be interred in national cemeteries for free. Vets groups can tell you how. Most funeral homes can also offer you other local sources.