Well the answer to your "subject" is: No. (but read on)
You can't do an ONT self-install. Installing FiOS in a typical residential setting as the fiber termination itself will require specialized tools as well as test equipment to insure the signal is being received properly (plus working with unterminated fiber is a job for the professionals).
So, if you live in an apartment which is not pre-wired and for which each tenant has an individual run from the street into their home (think small number of units and a lot of individual cable runs visible perhaps from an overhead installation), you're out of luck.
In larger multi-occupant buildings, most of these are pre-wired for utilities from a central location in the building. In this case, it may be possible to get service with a technician visiting -- but it will depend on if the central location is already setup as well since there is work to do there often as part of the install. In such installations, there may be an individual fiber run -- in which case you would most likely see an ONT already present somewhere in your unit since once installed, Verizon doesn't take them out. If you don't see fiber anywhere, then it is likely your are wired to utilize either MoCA or a DSLAM. MoCA would be available if they had individual ONT's in a central wiring location and individual Coax runs to your unit -- I have never seen such a setup although it's technical feasible. Most likely, you will have a DSLAM installation.. In. this case, the run FiOS into the central location -- distribute the TV signal to each unit via Coax (hint for a pre-run setup here would be cable is included for everyone with your monthly rent -- at least "basic" cable from Verizon) -- and. then the internet is run to your unit using a short distance DSL connection (in building).
This gets you service, but unfortunately your speed will be limited to DSL type speeds which aren't all that great.
Even then, this work is likely to require a technician visit to the central wiring room and I don't know if those are being done by Verizon at this point.
Short term, your best bet may be a traditional cable solution (and even then it may be limited in speed thru an in-building redistribution system). Perhaps consider a short term offering from them with a self-install and sort out the offerings with Verizon in the meantime.