Meter and time signatures are conceptual.
They are just categories of accent grouping.
Accents can be realized in various ways:
- dynamic (loud/soft)
- duration (longer rhythm is the accent)
- harmony (chord change coincides with bar line)
- you could abstract harmony further and just talk about pitch change (arpeggiating a chord can create a rhythmic/metrical pattern)
As long as something is providing accents you have the potential to create a metrical feel.
From a practical point of view, and moving up metrical levels, a common thing is to establish the barline with chord changes, establish some number of pulses per barline in beats, subdivide the beat by either simple 2 or compound 3.
Metrical feel doesn't just automatically happen. The composer needs to use musical elements to make meter emerge. A performer needs to play with good metrical feel. If composing or performing mishandles the musical elements, it can undermine the metrical feel.
Sometimes a composer can deliberately work against meter with devices like hemiola and syncopation, but when done right, those support the meter through contrast. Sort of in the way that dissonance works to support harmony.
Some music is unmetered. Medieval chant is a well known example. I've read that the unmetered aspect of chant was a kind of cultivated, high art endeavor meant to distinguish sacred music from secular music, which presumably at that time was metrical.
The take away is whether music is metered or unmetered musical elements must be controlled properly to achieve it, and not one, but several musical devices can be used to those ends.
...I'm trying to imagine a violin or piano just playing a simple melodic line—do we still necessarily perceive or feel a certain time signature or meter, absent non-metrical accents?
Sure. Just play some nursery rhyme tunes, like Twinkle, Twinkle Little Star or Pop Goes the Weasel. Even if you play those without any chord accompaniment, the metrical feel is clear. The pitch changes of the melody and the harmonic implications of the scale degrees used, and some chord arpeggiation in Pop Goes the Weasel, create the sense of barline, beat, and subdivision.