2003 Hyundai Elantra '03 Elantra hesitating on cold start

2003 Hyundai Elantra 2.0L w/ 93k miles. This car was recently handed down to us from my in-laws and has been working quite well except for this one thing: when the car sits for a long amount of time, usually 4+ hours, it hesitates when you start it up and press the gas.

I can rev it while in park, but then when I put it in gear, it might give one small burst of normal power, then it acts like you took your foot completely off the gas for several seconds before kicking in like normal. No changes are apparent despite pressing the gas down further, until it decides to kick in again. Again, it only does this after sitting for a while. I think it may not happen if I turn it on and let it sit for a little while, just when I try to go right away after turning it on.

It's not a serious issue for us at the moment, but I want to make sure it's not a sign of something more serious or costly. Any advice would be appreciated!