Your university will strongly recommend that you do not attempt to do this.
It's technically possible to visit the US as a tourist while intending to leave and return on your student visa, and many people have done this. US embassies will even advise that this is allowed.
You may also make your initial entry on the Visa Waiver Program (VWP) if you qualify. Those entering on the VWP must have return or an onward ticket out of the U.S. and you must make your intentions to enter only as a tourist clear to the inspector at the Port of Entry. Under either option, you must depart the United States prior to the start of your program and reenter on the student/exchange visa no more than 30 days before the start of your program.
What is not allowed in this circusmtance is to do something related to your studies when you enter under the VWP or B-2 visa. Spending time at the lab or looking for housing, for instance, are definitely not allowed. You are at a very high risk of being refused entry if you intend to do things of this nature, or if you are carrying evidence that suggests you may do these things (and on your proposed itinerary, you will be carrying such evidence).
Most all of the arrangements you will need to make with respect to living in the US while studying can be done remotely, or well within the 30 day window. Especially in university towns, it is possible to rent an apartment the same day you discover its availability.
If your advisor wants you to spend time at the lab prior to your current start date, you may wish to see if he can help you change your program start date to an earlier date. This will allow you to enter legally as a student earlier than you can do so now.