At the start of the Second Punic War, why didn't Hannibal engage Publius Scipio in Hispania, but crossed the alps instead?

Well, he wasn't the famous all conquering general of the history books as yet. Those victories were in the future. Taking the coastal roads is exactly what the Romans were expecting. That would work in their advantage, and against Hannibal's best interests.

The Romans would have much shorter supply lines, while those of Hannibal lengthened. It would be much easier for Romans to send in reinforcements. Even if they lost most of the engagements, Hannibal would find it more and more difficult to get more troops and supplies.

Apart from that, Hannibal couldn't simply march up and hope the inhabitants would join his cause. Many of them were Roman allies, and were not likely to change sides. In fact, it would be far more likely that the local population would prefer the Romans - if only because the Roman army was too close for comfort to decide otherwise. (Remember, this is before he crossed the Alps)

The area around the coastal roads was not Roman, but allied with Rome. Massalia was an independent Greek state, friend and ally of Rome. So was the entire area. Hannibal did know that Cisalpine Gaul was recently conquered by Rome. Instead of fighting his way through Roman held territory he choose to circumvent them and go there, using the completely unsuspected Alpine route. He'd have also to fight along the way (mainly the elements), but that was not a certainty. After crossing the Alps he would be in Cisalpine Gaul where he could reasonably expect to find allies and supplies.

The reason is that this was the Second Punic War. During the First Punic War the Carthaginians beat the Romans more than once, destroying their fleets...and the Romans built another fleet. This was what the Romans did. They did not give up just because they lost an army or a navy. They just raised another. And the First Punic War was not exceptional. A century earlier, when Pyrrhus of Epirus invaded Italy the Romans fought him and lost, and fought him and lost again. And fought him and lost again until Pyrrhus had to withdraw, having lost too many men to continue while the Romans just raised another army.

Hannibal knew that attacking a Roman field army -- a chancy thing, anyway -- would do little to win a war against Rome. They'd fight, Rome might win or it might lose. If Rome won, Hannibal was done, because Carthage was a sensible merchant city who would cuts its losses. But if Hannibal won, Rome would raise another army and fight him again. And again. And Hannibal couldn't afford a Pyrrhic victory, either -- too many losses and Carthage pulls the plug.

Under these circumstance, a battle against Scipio in Spain was at best a distraction and at worst a no-win situation.

Instead of planning to meet and defeat one Roman army after another, Hannibal decided on a strategic plan of invading Italy and separating Rome from its Italian allies whose manpower was a major source of those endless armies. (Many of those allies were recently conquered -- why would they be loyal?) Hannibal judged that if he could put a powerful army in Italy, and especially if he could win a battle or two, Rome's allies would revolt, and Rome would be forced to come to terms. (And, note, he never needed to attack Rome itself -- the plan was to isolate it, not to storm its walls.)

Of course, it turned out he was wrong. Even though he won huge victories at Lake Trasimene and at Cannae, all he achieved was a stalemate and the revolt of a fraction of Rome's allies. He was cut off, Rome raised new armies and found a great general in Scipio. Scipio invaded Africa, Hannibal had to follow, lost the battle of Zama -- and Carthage cut its losses and surrendered.

If Rome had been Carthage, Hannibal would have won.