Website launch vs. simply updating my website

I’ve spent the last couple months getting very clear on my niche and offerings, and also completely redesigning my website to reflect them. I’m just putting the finishing touches on my website, and I’m wondering now if I should work to create some hype/buzz around a new launch, or just simply publish it quietly to replace my old one. I don’t have a very large or engaged audience currently, and my goals for the last quarter of the year are to sell 10 1-on-1 coaching packages through offering mini sessions first (I’m thinking I’ll aim to do 30-40 mini sessions to guarantee success). I also want to grow my list from about 180 not very engaged or qualified subscribers to 400 very engaged and qualified subscribers by creating an awesome freebie/funnel and using FB/IG ads.

My question comes down to, is it worthwhile to spend time creating hype and buzz around launching my new website, or, for my specific goals, does it not matter so much? I really want to use my time wisely and also maximize opportunities (like launching a new website!) – any insight would be so helpful! Thank you!