Automated speech to text layer subtitles in After Effects
Assuming it's a video you are happy to make public, you could publish it through youtube and gather the subtitles from there as an .srt file.  

Be aware that automatically generated subs tend to have mistakes in them.

You could manually make subtitles using a free tool like Aegisub

Or you could pay a fee to a company like 3playmedia to generate the subtitles for you.

Once you have the subs as an .srt file:

Then to apply them in After Effects as burnt-in text, you could use a tool like PT_importsubtitles to convert the .srt file to timed text layers.