I suggest getting a lingerie bag and every time the socks come off, stick them in the bag.

https://www.amazon.com/Spasilk-Girls-Cotton-Footed-Months/dp/B07SFBSPQV/ref=asc_df_B07SFBSPQV/?tag=hyprod-20&linkCode=df0&hvadid=366282382731&hvpos=&hvnetw=g&hvrand=12253531423503701204&hvpone=&hvptwo=&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=9030102&hvtargid=pla-783797171979&psc=1&tag=&ref=&adgrpid=76464295575&hvpone=&hvptwo=&hvadid=366282382731&hvpos=&hvnetw=g&hvrand=12253531423503701204&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=9030102&hvtargid=pla-783797171979