The OP’s plan would be a rapid path to victory, assuming that the Italians begin their turn with everything they start their game with.
They don’t; most of the Italian navy gets annihilated turn 1, we refer to this as the Taranto Raid.
Also, their army can get shredded, that’s the Tobruk Raid.
If you have 10+ ground units, you may be able to just walk everything into Alexandria but under most circumstances, this is more like a dance back and forth taking and re-taking that area because neither UK nor Italy can make a stack big enough to deter a counter attack.
Germany could help, but the diversion of resources from the critical path (kill Moscow) isn’t wise, more fun.
Plan A
Take Southern France turn 1. (you could also build in Yugo but it takes much more time to build a factory then place units) Build some navy, have the germans cross.
Pros: you get a sweet Afrika Korps and if you work really hard at it, 1 or 2 bonuses for a few turns.
Cons: you lose the game because the med is a distraction, not a key zone, and after turn 5, you won’t be able to compete against the US with either Axis power unless you are spending most of your money to simply hold them off, rather than take the big money objectives and capital.
Plan B.
Attack a bunch of strict neutrals on turn 3. Instead of going for the heart of the allies, set up your troops at your border, and kill Sweden, Turkey and Spain all at the same time.
Pros: Now you own a bunch of extra territory and can cross direct to the oil lands.
Cons: you just made all the other neutrals hostile, wasted the initiative going in the wrong direction attacking a dormant power, and you spent the first four turns setting up a neutral crush instead of killing USSR. You have to attack all three of these simultaneously, or the allies can grab them, further increasing their power when you haven’t done anything to reduce it.