You can start to get interest from individuals at about 12 months, but usually they'll need to know you first to have something to convince them.
At two years you should be able bring on individuals relatively easily, but they'll be cautious. If you're good, you should be able to raise about $2MM this way within a fairly short period.
At three years you'll start getting legitimate interest from early adopter family offices, but many of them will either just test the waters with a small amount, or just follow your monthly progress for a while. They'd like to see you at closer to $5MM AUM before getting more serious.
At 3-4 years audited history and $10MM AUM, you'll be taken seriously by most family offices and high net worths.
Institutions (banks, endowments, pensions, etc.) won't even consider you until close to 5 years audited history and $20MM AUM. There are exceptions, but most of these are looking to allocate $2-5MM minimum and can't have more than a 10% interest in the fund. Frankly, regardless of returns, you just aren't worth their time.
Having said that, it all goes out the window with pedigree. If you graduated from Harvard, Columbia, Yale, etc. and worked for 10 years at Goldman, JPM, Credit Suisse, etc. then it'll dramatically speed things up. Also, if it is your second or third fund, and the first was a success, you can usually get interest just on hypothetical returns alone.