Some back-of-the-fag-packet maths.
goo.gl URls are 6 characters long, a-Z,0-9. That's a total of 62^6 combinations - about 56 Billion.
The realistic max length of a URl is 1,024 bytes.
That gives an upper-bound on the size of the database as 560TB.
Various sources reckon the average length is about 80 chars. Let's call it 100. So 56TB.
goo.gl only lasted 10 years (ancient for Google!). Bit.ly claimed to shorten 600 million links per month. I double Google was doing those numbers.
So…