My milk came in early does that mean labor is near

How long did you guys go into labor when your milk comes in early this is my first baby I am 36 weeks and 1 day today and I started leaking this morning and I was wondering does that mean labor is near has anyone else gone through this and had their baby in less than 2 weeks

Another thing I need some advice on is I am not breastfeeding any tips I do not want to send signals to my body to keep producing milk

Anything I should do in anything I should not do to prevent my body from producing more milk