I'm going to disregard any DM sanity here, and assume anything and everything published is on the table and can be mashed together...
Attributes - +10
- +10 from any attribute, because there are shenanigans that will allow you to get them to 30 involving combinations of attribute-increasing tome/manuals, Deck of Many Things Star cards, etc.
- Base bonus is therefore +10 from Dexterity.
Class - +33, +43 total
The starting 18s across the board allow for unlimited multi-classing, so we won't have any problems getting the build off the ground before we go hunting for shenanigans. You'll probably want to start with Fighter for the Heavy Armor Proficiency, because there's a solid bonus available only on a suit of Plate.
Feats - +5, +48 total
At some point, one of the classes needs to be taken to L4 to earn an ASI for:
Equipment - +8 minimum, possibly infinite.
Right off the bat we can get +5 from Scorpion Armor2. It would be beneficial to be a Yuan-Ti Pureblood, because Scorpion Armor tries to kill the wearer via poison damage each time they take it off or put it on.
A Stone of Good Luck gives another +1 to all ability checks, while the Ioun Stone of Mastery increases the character's proficiency bonus by 1, which benefits Remarkable Athlete. We can use one or the other, because we've got an attunement slot limit.
While we're talking items, you'll want something like a Sentinel Shield to grant advantage on initiative - the Weapon of Warning or Rod of Alertness are out because we are using our last attunement slot to embrace absurdity: add another +1d10 from the Sword of Kas, a sentient evil artifact sword.
Now, here's where it gets tricky... The DMG has minor magical properties that can grant an initiative bonus:
Guardian. The item whispers warnings to its bearer, granting a +2 bonus to initiative if the bearer isn’t incapacitated.
Let's say our particular Ioun Stone or Stone of Good Luck has it. Beyond that, it is ultimately up to the DM if other items with these properties show up.
The existence of this property means there is no theoretical ceiling - it doesn't have to be on attunement-required items. I know of at least two that exist in Adventures League play - a hand crossbow and a shield - and there may be more. There is the question of stacking effects, too. Is the Guardian property on two items the "same source"? That's up to the DM to decide.
Grand Total - +56+1d10... or more.
If we restrict the stats to more "normal" ranges, say 20s (for +5), it only drops to +36. No matter how you slice it, if you deliberately build a character with the express intent to "go first every time", you can overwhelm the variable d20 with static bonuses. Of course, the character may not have anything worth doing when they go first, and after the first round it doesn't really matter all that much.
1Being a Chronurgist also gives you access to Gift of Alacrity, a first level non-concentration spell that provides 1d8 to initiative for 8 hours. But that's temporary, so it doesn't count in the total.
2Both abilities here specify "that doesn’t already use your proficiency bonus". If you interpret using half the bonus doesn't count as "already us[ing] your proficiency bonus", then you could have both for another +3.
3If half-proficiency is acquired via Bard, there's room for Barbarian 7 for built-in advantage on Initiative from Feral Instinct, but you either wouldn't have Heavy Armor Proficiency to wear the Scorpion Plate, or you'd have to burn a feat for it.