Wild Magic Surge (or Tides of Chaos) is activated when you cast a sorcerer spell of 1st level or higher.
With the feat Ritual Caster you can choose Sorcerer and cast sorcerer spells without using spell slots.
Is there another way to activate Wild Magic Surge without using resources (ignoring time)?
Since your premise removes time as a factor, you can expend spells from a ring of spell storing and (depending on how your DM rules such things) potentially trigger the Tides of Chaos when that spell is cast. (How confident are you on rolling that 1 on a 1d20?)
The spells are prepped (typically during down time) and then off you go on an adventure with a loaded ring.
Wild Magic Surge says (PHB p. 103)
... your spell casting can unleash surges of untamed magic. Immediately after you cast a sorcerer spell ... the DM can have you roll a d20.
From the Ring of Spell Storing item description (SRD V_5.1, p. 237) :
While wearing this ring, you can cast any spell stored in it.
Casting spells and using Tides of Chaos are the only things that might trigger a Wild Magic Surge roll. There's nothing to indicate that casting a sorcerer spell as a ritual would exempt it from this, so that is certainly an option.
Two things to bear in mind:
The only sorcerer spells with the ritual tag in the PHB are Detect Magic, Comprehend Languages, Water Breathing, and Water Walk.
Both the Wild Magic Surge and Tides of Chaos sorcerer features are worded very specifically: when they are used, the "DM can have you roll ...". It isn't automatic, and it's entirely up to the DM.
So if your intent is to ritually cast Detect Magic over and over again until you generate interesting Wild Magic effects, that's only going to happen if the DM wants it to.
