Look at the positives - at mid 30s you will have more life and commercial experience, and more maturity, than many of your peers at SC level, so use that to your advantage. You should in any case be comparing yourself to your immediately senior grade, not your own peer group, to progress quickly - the old adage about acting like you are doing the job you want. One of the best things about your progression will be that consulting enables you to move past your peers quickly - you dont need a vacant seat to move into, so your destination point doesnt need to be in your direct reporting line. Network heavily internally, and use your age to built bridges with your life peers not your grade peers - a Manager in his mid 30s is more likely to 'bond' with you than he is with someone in their late 20s.
Also look at your industry experience and how you can start to spin out points of SME from it for projects. Chances are your younger peers wont have this, so you can outstrip those working off a consulting only tool kit quickly with a bit of application and thinking through how you could make this known/useful in the firm.
Plenty of positives!