Dad passed away a few wks ago. We have the Last Will and Living Trust. It''s just us 2 girls as the beneficiairies and it is split in 1/2

We read that FL law requires that the Living Trust must be filed by trustee. Our question is that dad''s property and bank acct is in dad''s name only as he never really thought of putting the bank acct or property under Trust name or pass on to beneficiaries. so with this, can we get the property legally transfer to us and same for the bank acct if we have the NOTICE of TRUST file? or we would have to have the Living Trust filed and just skip the NOTICE of Trust since we are filing the Living Trust if that is what is needed to be done for it to go thru probate so we can get ownership of the property and bank acct? If so, would we just go ahead and file the WILL at this point since that cost less for us to file in the state of Florida? Dads estate is less then 40K so we read up that we can file SUMMARY ADMIN to get the Will into probate. so to get the bank acct and property out of our dad''s solely name, can we just get the NOTICE OF TRUST file and that would be suffice ?