My neighbor was determined to get a baby because of the relationship she thought you could only get by raising a baby.
She saw me snuggling with my amazon and said, "That's the relationship I want!"
- so I reminded her that particular 'zon came to me at 8 years of age [and only a few weeks after I put my prejudice against amazons aside]. Technically, he came to my husband, but the 'zon had definite ideas about his next companion & he picked me.
You don't need a baby & you don't need a specific species. You need a compatible personality & "Mr. Right" is easier to identify in a rescue, where he [or she] already has a fully developed personality.
[My neighbor is now the companion to 3 rehomed parrots & doing a great job with them. One of her flock came to our notice on this very forum!]