Can H+ ion exist independently?
Be aware that $\ce{H+}$ is nothing else then a proton $^1_1\mathrm{p}$. Protons have an extreme charge density, typically $10^{15}$ higher than  any other ion ( but bare electrons or atomic nuclei).
Protons can exist free in vacuum or plasma, but even in gases they quickly react with many gaseous molecules, forming molecular ions, like dioxidanylium $\ce{O2 + p -&gt; HO2+}$.
Protons act in aquaeous environment as extremely strong Lewis acid with an electron pair of $\ce{H2O}$(Lewis base), forming a ion called hydronium, a particular type of oxonium ions.:
$$\ce{p + H2O -&gt; H3O+(aq)}$$
For convenience, we often use notation $\ce{H+}$ or $\ce{H+(aq)}$, supposing it is at least $\ce{H3O+(aq)}$.
Experiments mentioned in the above Wikipedia link confirm hydronium is usually coordinated with 6 water molecules as $\ce{[(H3O)(H2O)6]+}$, but multiple various hydration structures have been observed or assumed, like
Zundel ion $\ce{H5O2+}$,
$\ce{H9O4+}$($\ce{H3O+ . 3H2O}$)
or a cluster $\ce{H3O+ . 20 H2O}$
Note that the hydronium ion forms solid salts with acids with dissociation constant $K_\mathrm{a} \gt 10^{9}$.
E.g. a crystallic monohydrate of perchloric acid is hydronium perchlorate $\ce{[H3O+][ClO4-]}$