Working FT in another role before Investment Banking?

I recruited a year late for SA and got the internship at a good shop for the summer after I graduate. Issue is, I interned in a big 4 consulting group and received a full time offer there as well. Ended up signing the consulting gig, so I'm due to start working there right after my IBD SA stint in fall 2023.

The full time offers at the bank I'll be interning at will be for the following fall, in 2024, with no possibility of an earlier start date.

This would mean that I would be able to work for about a year at the consulting firm before hopping ship to my full time investment banking role.

Question is, would this raise any red flags or make it so that the bank would rescind my offer if they find out I'll be fully employed before starting?

Side note: My rationale for doing this is simple-- I loved the firm I worked at and they're paying me handsomely to essentially learn. I plan on giving my full effort for the year I plan to work there. Long-term, I want to work in Investment Banking, but I don't see the point of giving up a year's worth of employment and learning since I'm fortunate enough to not have to.

Not sure if I should get this plan cleared by the bank or to keep it a secret and mind my business (since I don't believe this harms anyone, people leave firms like the consulting firm I'm at within a year all the time). Right now, I plan on just keeping my mouth shut and letting each opportunity run its course, but I'm afraid if shit hits the fan and someone finds out at either place, I'd be labeled as dishonest. What do you think of this situation?