The answer to a "proper" expression for underground floors is that there is no standardized nomenclature, rather, there are multiple different designators depending on the place in question and the country: https://en.wikipedia.org/wiki/Storey#Subterranean_floors
The numbering of levels below ground is also quite varied, even within the same country. In English-speaking countries, the first level below ground may be labelled B for "Basement", LL for "Lower Level" or "Lower Lobby", C for "Cellar" or, in the case of the Andy Warhol Museum in Pittsburgh, U for "Underground". In British buildings, LG for "Lower Ground" is commonly encountered (or lower ground floor).
If there is more than one basement, the next level down may be marked SB for "Sub-Basement". The lower levels may also be numbered B1, B2, B3, B4, B5, B6, B7, B8, B9, B10, etc.. Negative numbers are sometimes used: −1 for the first level below ground, −2 for the second one, −3, −4, −5, −6, −7, −8, −9, −10, etc. Lettered levels are also sometimes used: A, B, C, D, E, F, G, H, I, J, etc.
In Hawaiian, these levels are numbered I1, I2, I3, and so on. The "I" stands for "Ilelo", meaning basement.
Of course, that's not to say that people won't understand you if you use first floor underground, but I think the reason this isn't widely used is because it's just a mouthful. Five syllables, versus the three syllables of basement 1, or first basement.
First floor underground has been used, though, and can be found in various engineering books, particularly in the English translation of Chinese manuals:
Code for Fire Protection Design of Buildings
"If they are arranged underground or semi-underground, they should be arranged on the first floor underground but shall not be arranged on the third floor underground or below."
The 2nd International Symposium on Rail Transit Comprehensive Development ...
"Commercial space is located on the podium and the first floor underground, while the commercial apartment is located in the high-rise building on the north side."
Advances in Civil Engineering and Building Materials
"The first floor underground chooses the zoning control combined with the light tube during the day and close corresponding area lights and it is open the evening. The second floor underground is also lighting for garage."
"These two were the ones who said they wanted to stay on the first floor underground"
Civil Engineering in Japan, Volumes 6-8
"View of the illumination towers from the vicinity of the taxi station, the first floor underground."
CCDI Architecture: Interaction with a Complex Context
" The commercial building comprises the main department stores and retail business, with the supermarket and retail space on the first floor underground."
Re/collecting Early Asian America: Essays in Cultural History
"The first floor underground was the home of the "number two" employees. In the Chinese social code actors belonged in the lower strata."
...and more can be found in Google Books
Ngrams shows that basement floor is the outright winner compared to underground floor/floor underground/basement level/floor basement/lower ground floor/lower lobby/lower level floor/lower floor level/sub-basement/subbasement/sub basement. I didn't include lower level because the results would be corrupted by the common definition of level.