Shouldn’t be an issue if you have enough winds on the peg. Typically when you don’t have locking tuners (an upgrade I *highly recommend* for ANY guitar!), you want at least two winds on wound strings (EAD) and 4 or 5 on plain strings. If the winding is removed from one of your low strings, to where only the plain steel is around the tuning peg, then 4-5 because at the peg, it’s a plain steel string.
Are they new strings? Are they properly stretched out? Stretching new strings is, to me, the most stressful part of restringing a guitar, even after 35 years I get some measure of anxiety from it.