unable to perform BIOS update

[iwis]

hello, I cannot update the BIOS of my HP Pavilion laptop - 17-g121wm (ENERGY STAR)
I tried all the methods in the guide but each time there is an option missing.
guide: https://support.hp.com/fr-fr/document/c00131952

1- the first method via the file manager, firmware is missing with me. I suppose it is due to the version of win10 .. I use win10 family V1903 and I can not update because the bios is not up to date except put via the usb boot

2- the second method, the HP assistant does not find a bios driver yet on the site there is an update.
current version of my bios: BIOS version / Date American Megatrends Inc. F.13, 06/08/2015
updated version: in picture / link: https://support.hp.com/fr-fr/drivers/selfservice/hp-pavilion-17-g100-notebook-pc-series/8499304/mode...

3 - the third method gives me this error "" "There is not enough free disk space to complete the system bios and firmware update operation. Delete some files to free up space disc then try again "" "". Basically it's a space problem with + 20GB free in the C drive and ten in the others. I don't know how much you have to free up for it to work!

4- the last method by usb boot is a waste of time because in the diagnostic tool (F2) there is no bios manager or any other name. just memory test, disk test, language and quit what gives me a glue. I looked everywhere but I found nothing.

without the update of the bios I cannot do any direct update of WIN10. each time I have to go through USB BOOT which causes me to lose application and data. if you have a solution to my problem, i am taker.

[iwis · Accepted solution]

problem solved or almost.
I was able to update the BIOS and then update win10. I had an idea and it worked.

to solve the problem I made a cumulative update of the BIOS from the oldest version to the most recent and it worked but the latest F54 version of 2019 still shows the same problem of insufficient space but currently I was able install the penultimate version F45 which is more than enough to access the win10 update.