If you're broke, how much do you realistically need invested for it to “matter” long term?

I’m currently pretty broke but trying to think long term. I'm 33 and I only have about $2K saved up.

I know the standard advice is “just start investing,” but I’m trying to understand this more practically.

If someone can only invest small amounts (like $50–$200/month), does that realistically compound into something meaningful over 10–20+ years? Or is there a threshold where the math actually starts to make a noticeable difference?

For example, at what invested amount does compounding start to feel impactful? Should someone in a tight financial situation focus more on income growth first before investing heavily?

Not looking for get rich quick ideas, just trying to understand what’s mathematically realistic if you're starting from near zero.