If DCS had been alerted that you there was a pending inheritance, they could have asked for a lien on the house at the time of your mom's death. They can do that any time up until transfer of title to a third party occurs. But, you don't actually say that happened. If that DID happen, then the State will collect that back child support.
Trusts can be used to shelter a person from FUTURE creditors. However, under the Uniform Voidable Transfers Act (RCW 19.40) , if a debtor transfers their funds to a person or entity to avoid payment of an existing debt, that transfer might be VOIDABLE. Meaning, the transfer to the trust can be disregarded or voided.
If you MOM had placed funds for you in trust before she died, and said “funds to remain in trust until adult child turns 65”, that is not a fraudulent transfer.
But, if you put funds in a trust for YOURSELF, and you maintain control over those funds, then I would say you should meet in person with a lawyer to get a thorough explanation of trust laws because I think that transfer may not be protected.
If you have the means to pay your past due child support, I would encourage you to just pay it. If you set up a trust, you may end up paying a lot of legal fees to defend yourself in court and then have to pay the support anyway.
But, you should get a consultation and whatever steps you take should be taken with your eye open.

In general, the State of Washington requires biological parents to provide financial support for their biological children.
https://app.leg.wa.gov/RCW/default.aspx?cite=26.18