Is this a problem?
It's not uncommon, IME, for a quiet person to still be having fun even if they're not contributing to every scene. Quite the opposite, actually: being forced to contribute can be stressful. It's probably worth checking in with your player - outside of game time - to verify that this is a problem.
It sounds like it is, and I'll assume it is for the rest of this, but it's often worth confirming.
Do the other players realize they're doing this?
I obviously don't know what the dynamics are at your table, but I've seen plenty of players (myself, unfortunately, included at times) who simply don't realize that they're dominating or monopolizing table time. If the "problem" (using the term extremely loosely) players don't realize that they're dominating screen time, mentioning it outside of table time can work quite well, especially if paired with a little GM attention to the quieter players.
If the "problem" (again, loosely) players are stepping on other players intentionally/maliciously - you probably need to have a conversation with them about not doing that. ... and, possibly, about dis-inviting them from the game, especially in the "maliciously" case. This is uncommon, IME, but is included for completeness.
What can the GM do at the table?
Many systems have explicit rules for entering initiative order for combat. As mentioned in the question, those systems can often be used for non-combat encounters.
... but, sometimes the initiative system is clunky for non-combat encounters or may have unexpected/undesirable consequences if used when battle erupts (eg., D&D3.5's surprise round or any effect that relies on a creature not having acted in combat yet).
Pseudo-initiative.
I've had good experiences - on both sides of the screen - with "pseudo-initiative". Basically, go once around the table before the clock ticks.
Navigating the wilderness? The clock might only tick once a day, but everybody should have the option of doing a thing that day.
Negotiating with the king? The click might tick once per point (which may include a little back-and-forth; pseudo-initiative is flexible that way), but everybody should have the option of doing a thing while that point is under discussion. For example: the dashing rogue may have a short dialog with the king while discussing payment for the king's request; everyone should have the option of interjecting with "that's far too low" or "I stab the king" before the payment is finalized and the discussion moves on to discussions about what resources are available before venturing forth.
In-person, this can often be accomplished by simply glancing around the table, making eye contact with each player; if anybody wants to interject, the eye contact is usually sufficient "permission" for them to do so. For some players, eye contact may not be desirable or sufficient; it may be preferable to augment or replace eye contact with a short verbal cue ("Jim? Sally?"). If "Jim" or "Sally" doesn't have anything to add, a quick "nope" will let the scene move along without feeling like there was an interruption.
In virtual settings, the verbal cue is probably required, along with a sufficient pause to account for a moment's thought and Internet lag. This can break up the scene a bit more, so you might want to ask them to...
Raise your hand.
It's cheesy, but everybody knows that someone whose hand is raised wants to say something. Remind your players of this, and reinforce its use by moving to the person whose hand is raised as quickly as practical.
Some online products support raised hands explicitly, but not a lot. Most voice chat apps and virtual tabletops have a text chat capability; putting "✋" or something in the chat can work if somebody's paying attention.
Regardless: like with pseudo-initiative, the raised hand's owner should be able to interject before the clock ticks. If that requires some slight ret-conning, well, that happens some times.