Dexterity (relative PHB pg. 177)
Initiative - At the beginning of every combat, you roll initiative by making a Dexterity check. Initiative determines the order of creatures' turns in combat, as described in chapter 9.
Surprising Foes (supportive PHB pg. 183)
If the adventurers encounter a hostile creature or group, the DM determines whether the adventurers or their foes might be surprised when combat erupts. See chapter 9 for more about surprise.
The Order of Combat (supportive PHB sidebar pg. 189)
- Determine surprise (DM controls if / when this happens)
- Establish positions (DM controls setup of PC and mobs)
- Roll initiative (PCs roll individually, DM rolls for groups)
- Take turns (surprised do not act on first turn)
- Begin the next round. (restart initiative, surprised now can act)
Surprise (supportive PHB pg. 189)
If you're surprised, you can't move or take an action on your first turn of the combat, and you can't take a reaction until that turn ends.
Initiative (relative PHB pg. 189)
Initiative determines the order of turns during combat. When combat starts, every participant makes a Dexterity check to determine their place in the initiative order.
Help (relative PHB pg. 192)
You can lend your aid to another creature in the completion of a task. When you take the Help action, the creature you aid gains advantage on the next ability check it makes to perform the task you are helping with, provided that it makes the check before the start of your next turn.
- Surprise is established before combat ✔️
- Dexterity check for Initiative ✔️
- Dexterity is an ability check ✔️
- Advantage on ability check ✔️
- Give another party member advantage on Initiative roll ✔️
The OP is talking about Help and Initiative so those are relative, anything else is either supportive or moot.
There is no more surprise round. Surprise happens before combat is even started. If a character or more is surprised, then don't act during there first turn.
Initiative means combat has already started, so a PC would not gain surprise, only benefit off the top of my head is Assassin class feature Assassinate gain advantage on creature who haven't taken a turn in combat yet.
In actuality, with you "Helping" the other player, you as a character are distracted from Perception (passive/roll) to notice surprise.
There would need to be some RP or another ability check i.e. Perception like mentioned previously and not metagame talk of "I use Help action to give the Rogue advantage on Dexterity check for Initiative"