Our 6 month old wakes up exactly when my 6.15 alarm goes off

Writing this at five because today he beat the alarm. For about three weeks he has woken at 6.15 on the dot, which is when my alarm rings for the office commute. I moved it to my phone on vibrate under the pillow. He still wakes, I think from me getting up and the bathroom light. My mother says he would sleep till 7.30 if I could leave without a sound. The caregiver comes at 8 and would rather he was up and fed by then anyway. Is it worth trying to shift his wake-up time, or does the household simply start at 6.15 now?