That’s a 24 volt fan it’s 100 mA running there no way a 1.5 AA boosted to 24 V will run that

 

There is no "standard" 4020 as that is just a physical size (40mm x 20mm) and they come as axial and radial fans.
Really need part numbers and datsheets to help you.
That said, there is a 5V 4020 radial fan on Amz that states it requires 0.2A (1 W).
Assuming 80% efficiency for your DC/DC, you need 1.25W and with AA at 1.25V, that's 1A.
typically for alkaline AA, at a load of 1 ampere, which is common for digital cameras, the capacity could be as little as 700 mAh )
That give run time on 1 AA of 0.7 hours or 42 minutes, BUT the voltage supplied by battery will droop and the DC/DC will probably cut-off sooner.
Looked up your DC/DC as best I could and one looking very similar, the user was only able to get 0.1A out at 5V. This converter may not be able to supply the amperage you need.
You may also try connecting 2-AA in series to provide 3V into DC/DC to see how well that works.

 

Looking at Amz versions, they appear to use a 2108A IC and reviewing the datasheet for a ME2108, it looks like to get any decent performance you're going to have to use a 3.0V input which is 2 AA batteries in series. Try this and let us know if fan runs......

Also, consider adding 10 - 47uF cap on the output side.