Since Adobe Illustrator supports the DWG format, the natural choice here would be to use this program to convert AIT to DWG format. Probably no other programs accepts AIT templates so, it may be actually the only choice.
Convert Adobe Illustrator template to AutoCAD drawing.
We found 2 software records in the database related to .ait to .dwg file format conversion.
Microsoft Windows software - convert ait to dwg on Windows
A powerful vector graphics editor from Adobe
Convert from ait file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned ait to dwg. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
Apple macOS / Mac OS X software - convert ait to dwg on OS X
Mac version of Adobe's vector graphics editor