You technically can, you just need tons of money and knowledge (or even more money to hire people with knowledge)

To explain better, an ASIC is a specific integrated circuit you design and fabricate.
For making one, you will usually need a team of engineers working full time, you need specific software like Cadence that costs a fortune on license.
Once you go to fabrication stage, that is the most expensive part, because you need to go with a foundry (usually TSMC) and pay millions of dollars to get in production.
From the foundry you get wafers with many chips inside, which you have to dice, package, and test.
Then the chips go to a board with connections and cooling system.

Design phase may take up to a year. Fabrication takes 1~3 months.
I'm not sure about the cadence license, because I have free access in my lab, but I've heard the full suite is like $100k per year. The mask set for fabrication in TSCM 65-nm is about 2 million dollars and each silicon wafer has a price of $10k each.

Anyway, here I'm trowing at you some numbers I have in my head, some may not be very accurate since I'm student to I have all the above for free, but basically, if you want to make ASICs, you alone can't, you need to create a start-up to raise the funding necessary to cover all the expenses.