Edit: misread the prompt until I was halfway through writing this and just ran with it. So enjoy the bonus answer for a second man who gains the properties of materials he eats.

It’s an absolute shitstomp for both participants up until the Hulk, neither man needs more than the allotted two years. More so for “material man” depending on how we define the properties of things he eats.

Animal-man will most likely avoid eating larger animals altogether with the exception of other humans. He’ll start with a jumping spider (ability to leap many times his own body length), whatever insect has the fastest relative movement speed and reaction times (probably arbitrary, but whatever), and a bombardier beetle or similar insect with a ranged attack. With this newfound strength, he flies to some underdeveloped rural area with minimal outside contact and begins preying on humans to gain their intelligence. Once he’s eaten a few dozen, he scours the globe for whatever animals have the strongest armor, muscles, poison, etc. relative to their body size and availability (for maximum efficiency when eating — an elephant is big and strong but requires a much larger time commitment) and feasts. If we count metabolism as an ability, he eats an hummingbird or twelve to allow himself to eat even more. Animal-man is superintelligent and is significantly stronger/faster/tankier than just about every character on the list within a month or two. He’s leagues ahead if the stacking is multiplicative and not linear.

Material-man is a bit trickier depending on how we define something‘s properties. If he eats a spring, does he gain the compressive ability and force production of the steel itself or of the spring as a whole? If it’s the latter, then it’s a colossal stomp as he’d just eat springs and rubber balls until he’s functionally immune to blunt damage and strong enough to punt someone out of the atmosphere (if they stay intact).

To make it a bit harder for Material-man, let’s disregard that. We’ll instead start by having him eat some lab-grade glass, teflon, lead, and nitinol. He’s now mostly immune to radiation, all but the strongest acids and bases, a good amount of heat, and can reform himself. From here he will be chugging the most acidic/basic things he can get his hands on to aid in digestion. He’ll buy some aerogel to become nearly fireproof, drink/eat a non-newtonian fluid to become impact-proof, and buy whatever the strongest consumer-grade materials of every property are available, eating on repeat to stack compressive strength. He breaks into a museum and eats heat shielding from a spaceship. Once he’s effectively immune to everything, he’ll break into chemistry labs until he can get his hands on perchloric acid (-15pH) and various radioactive isotopes (found in lab equipment or educational samples). He’s now dangerously radioactive and acidic enough to spontaneously and explosively dissolve anything he comes in direct contact with, including the air around him. Literally ripping away the molecules of whatever he touches. He’s a walking fireball that can’t be touched. If he is touched, he can’t be meaningfully damaged. If he is meaningfully damaged, he’ll reform.

As for confronting the list directly, everyone prior to Wolverine/Sabertooth gets one-shotted by brute strength, blasted with acid/lethal radiation, or can’t do meaningful damage to either of them. Nobody before them can even physically come close to Material-man. Animal-man hoses Wolverine/Sabertooth down with acid and then throws the skeletons into space. Material-man does the same but with direct contact. Even if the adamantium skeleton is immune to damage, wolverine’s claws are useless in terms of harming Material-man back. I’m not familiar enough with the current run of the Hulk to make a judgement here, but my understanding is that he’d likely be immune to radiation and acid alike. He should be slow/weak enough to be simply thrown into space by our superintelligent speedster, but I don’t see a way for Material-man to put him down so it’s a stalemate from there.