Fuse Average time Current
Lets take an example: VNom= 12V DC Vmax = 13V DC INom= 2.5A Irush = 3A. Fuse should blow on any current over 3.25A (20AWG cable used).

There's your problem. Must carry 2.5 A, must blow on 3.25 A. That ratio is far too tight for a fusible fuse, unless you make some restrictive assumptions. Normally, fuses are used to protect against very heavy overloads like a short circuit, where the expected fusing current is waaaay above the must carry current.
You need to factor in what you are protecting, which will give you a time to blow. If you're protecting semiconductors or a loudspeaker, then you need under a second. If you're protecting wiring, then a minute should be adequate. Note that a nominally 1 A fuse takes almost two seconds to blow at 3 A. Those curves go up asymptotically to infinite time.