I'm sorry for your loss. You'll want an answer from an attorney permitted to provide you with advice specific to the state with jurisdiction over your father's estate, but here are some considerations.
If your father left a valid Last Will and Testament, you will want to determine if the individuals named as beneficiaries in that document are the same individuals who would inherit his estate if there were no Will. Most states provide for alternatives to formal probate proceedings, and a family that gets along always makes it easier. For example, even when a decedent leaves a valid Last Will and Testament, it may be possible and even advisable for the beneficiaries and heirs to agree not to incur the cost of having it admitted to probate.
Generally speaking, insurance proceeds often pass to designated beneficiaries independently of a decedent's Will. Most of the time, those beneficiaries need only provide proof of death to the insurance company along with proof of their identity when making a claim. If a part of the insurance proceeds pass to your father's "estate," you may be looking at a formal probate proceeding.
Likewise, bank accounts can be created and maintained in a variety of ways. They too can often pass to beneficiaries without relying upon a decedent's Will. If, for example, the account that you mention is "payable on death" or jointly-owned with another person, formal probate proceedings might be avoided.
One reason why formal probate proceedings might still be in your future is the absence or presence of debts owed by your father. You don't mention any, but some alternatives may not be available if there are creditors waiting in the wings.
Visit with an attorney that practices in the state where your father resided when he passed away, advise him or her of the facts you mention and ask if there are any alternatives to a formal probate proceeding that you might be able to take advantage of.
This answer does not constitute legal advice. I am admitted to practice law in the State of Texas only, and make no attempt to opine on matters of law that are not relevant to Texas. This answer is based on general principles of law that may or may not relate to your specific situation, and is for promotional purposes only. You should not rely on this answer alone and nothing in these communications creates an attorney-client relationship.