Create demand as a coach first, or go for my ideal rate?

I am creating a new 1-1 coaching package for my new business as a coach. My desired rate is based on my own needs/wants: a goal of 100K in my first year. I am available for 12 sessions per week, coaching is every week for 6 months so rate becomes around 4K€.

I aim to coach women solopreneurs to overcome self-sabotage and exhaustion so they become able to take inspired action and make more money as a result.

I have 3 thoughts:
1) “4K is a huge investment for them and I doubt anyone around me has access to that money to start with”. (also: I’m in Europe, where I live there’s no possibility to put the amount on a credit card; they have to have or get the money).
2) “I’m not established as a coach yet in that niche, so don’t have testimonials etc, proof that it works” (even on myself, because I’m doing the work at the same time!): how would they trust me?
3) I’ve heard this idea that, when you first start off, you need to create demand as a coach. And that this CAN mean lowering your rates instead of thinking “it’ll devalue me”, or “I wanna make more money!” – in other words, make it about finding clients and helping them first. And it makes sense to me too.

So I’m feeling conflicted about setting a price for my package. As a result, I stay stuck, don’t choose and commit myself to a price and don’t put myself out there as much as I could, offering value etc to attract potential clients and making offers.

If I go out at my ideal rate and it doesn’t work, I’ll have lost prospects (because I can’t go back to them and say “hey i lowered the price!”)

If I go out with a much lower rate to make it more accessible to begin with, I’m concerned about not reaching my goal, and that anyways before I’m really “in demand” and “sought after”, it will take sooo long, probably a few years in, until I’m able to have clients at this ideal price.

So do I go out with full/ideal price, or go out with lower price and build from there? Or is there another way to think to avoid that dilemma? Thank you!