It's a fair question that a lot of people are asking. I think it's far more more unlikely than it is likely that January dates get pushed back, as the shock of Covid has already hit. However, the possibility is always there. You should be safe.
These odds also dimish over time. I.e. It is more likely that Sep-Dec 2019 start dates are pushed back than Jan-Mar 2021 ones are. However, I do still believe pipelines have stabilised across most offices.
However, make use of your time! Assume you'll have a delay and you won't be disappointed
Send out feelers to see if you can snag an internship or part-time job...the extra experience, income, and backup, are all good to have.
Prepare for the GMAT/GRE (if higher education is any future possibility) - Igiven you've graduated recently, preparing for the GMAT/GRE will be much easier than if you do it later. Trust me! I took the GRE my senior year of college and did very well, but struggled significantly with my GMAT 5 years later. Testing skills get rusty!
Data Science is a growing, important, and marketable field that I highly recommend gaining skills in. You may not have to get a full certificate (though it is an option). There are many one-off classes that you can group together (i.e. a database design/structure class, SQL class, Python/Ruby, Tableau, Data insights/visualization, etc.)
Attend an academy to hone your skills - There are lots of academies out there that prepare you for the real world. Not a bad use of time to get skilled up so that you can hit the ground running at Bain and rise up the ranks even faster! (Feel free to PM me if you'd like to know of a few)