The stupid thing is that the landscaping gardener absolutely recommends this as the first step, even before establishing the terrace. Such rough work should definitely be done immediately and not messed around with later on the property with extensive earthworks.
But that doesn’t really surprise you, does it? Well, of course he wants to do it right away because then he’s sure to get the contract. He doesn’t get it if you do it in a few years, because the probability is simply higher that someone else will get the job then.
The advice itself is okay in that there may potentially be repairable (!) damage to the existing garden if you do it afterwards. But selling that as the necessary first step is total nonsense. That would mean, conversely, that he only installs pools in new builds... cheap and obvious sales tactic in my opinion.
If you want to do it later, and he can’t manage it, then he’s out. Surely there are others who won’t make such a fuss. As others have said, a mini excavator is enough, you can protect existing lawn if necessary, and possibly also repair it. I don’t understand the problem. Or is your property so special that you can never ever get back to where the pool is planned?