Actually, that is not true. Ships-of-the-line were being built in the New World prior to when the British colonies revolted in the 1770s. Most notably, Havana was a major shipbuilding port for Spain. They had built 80-gun SOLs in Havana in the 1760s, and 3-deck SOLs (MOW equivalents -- there was no real warship larger than a SOL) prior to the French Revolution.
The British colonies were turning out 44-gun two-deckers prior to the American Revolution (Falkland and America come to mind) as well as frigates. The French also built a proto-frigate or two prior to losing Canada in the Seven Years War (French and Indian Wars for you Amero-centric types). I say proto-frigates, because the true frigate emerged late as a warship type -- between the 1740s and 1760s. Prior to that small two-deckers filled that role.
The main reason the Colonies did not build SOLs during the American Revolution was more due to European intervention than inability to build them. The Continental Navy had laid down three, but abandoned two after French entry into the war made them unnecessary. Also those puppies were expensive to run, and the revolutionary nations (starting with the British colonies in the 1770s through the French and Spanish colonies as late as the 1820s) all had one common characteristic. Regardless of the potential wealth of the new nation, the revolutionary governments were all broke.
At one time American commissioners in Europe attempted to buy used SOLs from various European powers. They failed primarily because the nations that they were negotiating with (France, the Netherlands, Sweden and Denmark) thought that they might be involved in a war fighting Britain and wanted to hold onto their ships for their own use.