Lots of babies don't engage before labour including first ones.

I've done two births this month, both first babies that weren't engaged at the onset of labour.

I'd really encourage you to do some research into an induction - with your baby still high, your body may not be ready to labour and an induction will dramatically increase your risk of a caesarean.

And an induction at one day over your EDD seems a tad trigger happy if everything else is fine. Is there anything else going on that has your OB concerned? It's really important that you ask questions - don't be led into something if you don't understand exactly why it's being recommended. All the best.