You probably did not knew, but as alpha you can get actually 6 mil SP , you train to the 5 mil SP limit then inject the 1 mil SP you get if you joined the game using a refferal link .
To pass that 6 mil SP cap , you can use alpha daily injectors or even normal injectors up to the maximum alpha limit of 20 mil SP . Also you can subscribe , train to a target set between 6 - 20 mil SP and then relapse as alpha , and as long as you are below or equal to 20 mil SP , you will retain those skills (trained or injected) if those skills are alpha skills and to the allowed level as alpha .
On the page below there’s a list that explains it more in detail for you , there’s a table that you can expand there and it will show you skills you are allowed to train as alpha and the limitation:
https://wiki.eveuniversity.org/Clone_states
To play you don’t need to be omega necessarily . Some players are happy as alpha as you can even specialized more characters (with their limitations ofc) . There’s a lot you can learn by staying alpha for a while , it’s more important to learn game mechanics than having a bunch of SP at first.
Eventually , there will come a time when you will need omega , and it is what it is , you either subscribe or use the in game PLEX for that.