The feat doesn't say one way or another, so there's not going to be any rules citations that are all that specific, but the general assumption the game makes is that feats don't have secret invisible unlisted requirements. This is the sort of thing that often doesn't have very precise rules attached to it, as it's largely an RP thing.
The language used for regular familiars suggests that a mundane animal becomes a familiar, which suggests that in the general case, at least for non-improved familiars, you do need an actual copy of that animal. I would say that, in general practice, acquiring such a creature is generally treated as something that can happen without too much trouble during downtime. I've never heard of a DM making the availability of a mundane animal a serious bottleneck on a character acquiring a familiar. That's just convention, however, not a hard written rule.
Similarly, general practice is such that, if a player intends to take Improved Familiar, either the creature just sort of shows up around the point where the player is taking the feat and is now the familiar, or the DM collaborates with the player to introduce such a creature as an NPC with the intent that it will soon become the PC's new familiar. Sometimes the character simply petitions the powers of an appropriate outer plane to send an appropriate creature. I have also seen the feat fluffed as the PC's old familiar taking on a new form or "revealing its true form," although that's a half-step from what the feat directly suggests. (Although in some cases, as with the Chosen One paladin archetype, this is explicitly what happens.)
Ultimately, it's up to the DM, and generally a DM's role is to make sure that the group as a whole is having fun. Improved Familiar is a good feat, but it's not one where the intent is that its use is gated around having to actually somehow acquire an imp or whatever.
As a GM, I dislike the improved familiar just appearing, so I work it into the plotline. It could be a friendly creature encountered in a dangerous dungeon, it could be a gift from a benefactor, etc.
For example, in my current campaign, when the bladebound magus leveled up to 3rd level and gained his blackblade, he found a dead adventurer that had a blackblade and claimed that blade. The player and I worked out the background of the intelligent blade and the blade gave the party a description of a part of the dungeon that it had seen but they had not yet entered. Likewise, when the bloodrager in that party took improved familiar, she encountered her clockwork familiar in a group of robots that the party had to fight and they took an immediate liking to each other. In contract, when the skald gained a lyrakien skald cohort via Leadership rather than as an improved familiar, the lyrakien had heard tales of a more experienced skald and had sought her out to become her apprentice.