Many states have a simplified procedure for small estates. Some states have a small estate procedure for probate and then a summary administration procedure for estates of "intermediate value". Court clerks cannot give you legal advice, but you should be able to determine if his possible estate fits within small or summary estate guidelines via a phone call to the local probate court. In CA, a small estate would have a total personal property value of less than $100,000. If any of the property is real estate, the value of that real estate cannot exceed $20,000. (My info may be a little dated, but that should give you a general idea of what might be considered a small estate.)
That being said, proceeds of life insurance, 401k, 403b plans, retirement plans, etc., generally bypass probate. If he had such accounts, he should have filed a designation of beneficiary for them and that is who is likely to receive the monies, if any, in such accounts.
The adoption should have terminated his parental rights. His biological daughter is a legal stranger and, in most states, would have no legal standing to inherit anything under instestacy. Ex-wifes generally do not qualify either under intestacy.
However, that leaves other next-of-kin in line to inherit. Did he have any siblings? Is he survived by a parent(s)? They are going to be in line way ahead of you.
Even though some of his assets may not be subject to probate, getting those letters of administration might allow you to acquire info about them that otherwise would not be available to you. So, it may be worthwhile to you to get those letters just so you can waive them at the local bank or send a copy to the state retirement plan, insurance company, etc.