The mishnayot in the first chapter of Sotah describe the beginning of the process -- the accusing husband brings her to the court where they try to intimidate her into confessing, and if she doesn't they take her to the temple gate and begin humiliating her (loosening her hair, baring her breasts, etc). In 3:3 it then says:
If she said, "I will not drink [it]" before the scroll was erased, the scroll is archived, and her meal-offering is scattered on the ashes. [...] [However,] if the scroll was erased and she said, "I will not drink [it]," we force her mouth open and make her drink against her will. (Sefaria translation)
By this mishna we have a "deadline" after which she can no longer refuse to drink, but how early can she refuse and abort the whole process? If she says from the time her husband first brings her to the court that she will refuse, do they go through with the intimidation and humiliation anyway?
On the one hand, maybe they do because they hope it will get her to confess. On the other hand, the humiliation is at least immodest (as well as embarrassing), so one might think that if they could avoid unnecessary immodesty they would.
The mishna describes a sequence -- the man brings her, the court intimidates, they bring her to the gate, etc -- and I can't tell from when "if she refuses to drink" applies. (It's only mentioned after they've written the curse.) I'm not saying they would want to humiliate her if she's already refused, but maybe they're required to (just as the man is required to bring her if witnesses have testified that she was secluded after being warned).
If she refuses any time before they erase, the outcome is the same -- she's divorced without her ketubah. Given that, how early can she "jump" to that outcome?