Is it possible to build an H-Bridge with only N-MOSFETs (and these other components)?
Without even considering the concept of bootstrapping it is totally possible to build an H-Bridge with N-Channel MOSFETs in both the upper and lower switch positions. This is done all the time in high power drivers due to the much larger selection of high performance N-Channel FETs over that for P-Channel FETs.

The key parameter to keep in mind is that the gate drive voltage for the upper FETs needs to be driven above the output voltage positive level by a good amount to ensure that the upper FETs are turned on fully. A starter way to achieve this is to provide a higher voltage supply rail for the gate drivers than what is used for output positive voltage rail.

Once you have learned and understood the concepts of what it takes to drive the upper N-Channel FETs with sufficient gate voltage you can then begin to investigate how to get that higher voltage without having to provide an additional higher voltage power supply. One way to do that is to build a charge pump circuit, with some of your other components, to "double" the positive voltage rail up to near 2X the voltage. To utilize this higher voltage will require a circuit that can swing the upper FET gate up to this 2X voltage and then low. The Op-Amp would be a good candidate to do that for you. 

In the industry there is a tendency for engineers to be tasked with designing circuits that cost less but give desired performance and function. There is technique called boot strapping that uses the switching action of the H-Bridge itself to drive a capacitor in a simpler form than the completely separate charge pump circuit. The bootstrap capacitor can achieve almost twice the positive voltage rail level of voltage and again provide the necessary gate drive bias for the upper N-Channel FET. We never get anything for free however and in this case the simpler bootstrap circuit has the requirement that the H-Bridge needs to keep switching all the time to provide the pumping action. This means that a motor drive would need to be switched PWM type drive and never get to full 100% ON drive level.