Sonos is about filling rooms with music rather that headphones, so no, Sonos gear doesn't have headphone sockets.
The Apple earbuds are low impedance medium-sensitivity headphones. That means they're relatively easy to drive and they go reasonably loud from a single unit of input power. So if they aren't loud enough then it's either not enough power from the source device or the fit of the earphones in your ears doesn't make a good seal so you're losing some of that volume. I suppose the other possibilities are that your hearing is knackered or you just like insanely loud sound
The solutions then would be to twofold
(a) address the fit of the earphones either with better quality earbuds (Etymotics or similar) or earphones with large over the ear type pads that form a better seal against your head.
(b) sit a device (a headphone amp) somewhere on the output of the turntable after RIAA equalisation to boost the output power. In your case your TT plugs in to the line in on a Sonos Connect so the signal has been RIAA corrected at the output of the turntable. You probably have a switch marked Phono-Line and it is set to Line.
For reference the specs I have seen for Apple earbuds are roughly 40 Ohm impedance and have a sensitivity of around 109dB per mW of power. I think you'd have to search very hard to get much higher sensitivity than that with an over-the-ear headphone but you might do it with an earbud.
For headphone, the low impedance high sensitivity route work best for 'phone that are to be driven by battery powered portables. Once you start looking at mains powered headphone amps then your options on 'phones open up considerably. A mains powered headphone amp will provide a lot more power, so it is possible to drive high impedance phones (600-ish Ohms). In a like-for-like design the higher impedance version will sound better.