Kentucky might not be so far off.....There was a group of Adams in Smith Co TN who had children born in Kentucky....Macon Co Tn was at one time part of Smith Co Tn.
Go to the Genweb page for Smith Co TN and in search type in Adams.....look at Cal's Column and he talks about 3 different groups of Adams who lived in Smith Co....one of these groups seem to have been at one time in Kentucky.
I am trying to sort out the Adams in Smith Co Tn ca 1812 and having a rough time of it.I have the Adams from the 1820 and 1830 census.
There were 3 marriages between my Turneys and the Smith Co Tn Adams, 2 of them going to Arkansas where the name Pleasant was used a lot.
So your Adams might have been born in KY, then to Tn, then to MO as it seems some of them did.
So you might want to look at some of those very early Smith Co TN records (Dekalb, Cannon, Macon and part of Wilson were then in Smith).
One group came out of Patrick Co VA around 1809 to Smith. One group seems to be out of eastern TN.1806 there was a Jacob Adams with property in Hawkins Co TN near my Turney who about 1804 went to Smith Co..... There was an Adams on Cumberland - so early settlement of Nashville.And so on.