Hi bnorsworthy,
Thanks for using Apple Support Communities! I see you have a question about recording audio messages in Messages app, and I'd like to do what I can to help.
Do you find this happening with every contact in Messages? Or just one person?
Does this happen with Wi-Fi and cellular data?
Have you restarted your iPhone since noticing this issue? If not, go ahead and do that, as a restart can resolve unusual issues.
Restart your iPhone
With that being said, I tested this on my iPhone 11, and it does seem that iMessage needs to initialize the audio recording function for 2-3 seconds. Since you are not having the issue with a recording app, it does look like this could be expected. The screenshots in this article, also show a few seconds of a bar at the beginning also: Send photo, video, or audio messages on your iPhone, iPad, or iPod touch
Take care!