To put it simply, it would have been a disaster to invade through Sicily during Punic 2, as the Roman navy would just swat down troop transports due to their well established naval superiority following Punic 1.

Let’s start with some context in Punic 1. Let’s first take into account where the balance of naval superiority first begins to shift from originally Carthaginian hands to Roman hands. Following the resolution of the battle of Agrigentum, (this is controversial, more on this in a second.) Polybius states that the Romans seize a shipwrecked quinquereme and reverse engineer the design to their own strengths with the Corvus, a ladder mechanism used to send legions across to board the other ship (it looked somewhat like this.), in contrast to the commonly seen ramming tactic commonly used by the Carthaginians. However, historian Clark Reynolds argues that the Romans had experience with naval combat before this to fight off pirates-- I have cited the book it’s noted in down below, it’s on pg.22 if you can get your hands on it online or on paper. I personally somewhat buy this, as he argues that Syracuse could have theoretically shared naval technology with them. (Please PM me w/ questions anyone may have regarding this book, I can type the quote verbatim if you can’t get your hands on it :) ) Anyways, point being, Rome had access to quinqueremes during Punic 1.

Furthermore, Roman naval superiority generally began in Mylae, a naval engagement north of Sicily, offshore the coast of present-day Milazzo. Polybius states somewhat strangely that the Carthaginians had exactly 130 ships. (It seems a little too perfect of a number, but who knows!) Rome is said to have somewhere around 90-115 ships, but what we can infer from these numbers was that Rome was outnumbered. On the Carthaginian side, Hannibal Gisco commands the fleet. Gaius Duilius (I lost my glasses, so I hope this is spelt correctly…) commands the Roman fleet. From my readings, Hannibal assumed that the aforementioned corvi couldn’t pivot. They could. So, Hannibal attacks solely from the sides/rear to avoid the Corvi entirely, but, as I said, they could pivot, allowing masses of Roman soldiers to board Carthaginian ships. Polybius says that around 13 ships sunk entirely, and 30 ships were captured, resulting in a decisive Roman victory. Hannibal would later be crucified for his incompetence at this battle.

Consequently, Rome began to gain significant naval superiority, to the point that it was hazardous at best to even attempt a Sicilian invasion.

Carthage tried to launch a few naval raids against Lilybaeum but they were always decisively repulsed. It likely would have ended up in complete disaster if a Sicilian invasion was to occur. As previously stated in this thread by LegalAction, the Romans were pretty heavily barricaded in Lilybaeum-- so they expected this. Longus was eventually recalled from Sicily, however. Most any and all communication to Hannibal that attempted to cross to Sicily was swatted out by the Roman navy, as well.

Sources

Adrian Goldsworthy, The Punic Wars

Clark G. Reynolds, Navies in History.

Livy, book 16-19

Livy, book 21-29

Polybius, Histories, 1-3