Why did Heth go towards Gettysburg on July 1, 1863?

tl; dr

While obtaining supplies (including shoes) for the army was an important objective, Heth's advance into Gettysburg was a reconnaissance in force to determine the actual composition of Union forces that had been observed in Gettysburg by Brigadier-General Pettigrew on 30 June.

The evidence

In his report following the Gettysburg Campaign, Major-General Henry Heth wrote the following:

On the morning of June 30, I ordered Brigadier-General Pettigrew to take his brigade to Gettysburg, search the town for army supplies (shoes especially), and return the same day. On reaching the suburbs of Gettysburg, General Pettigrew found a large force of cavalry near the town, supported by an infantry force. Under these circumstances, he did not deem it advisable to enter the town, and returned, as directed, to Cashtown.

Now, it is important to remember that at this point, a large part of the Confederate cavalry, and their best cavalry commander - J. E. B. Stuart, had been deployed on a raid intended to pass around the rear of the Union army. This raid has been the subject of ongoing controversy and debate ever since the battle, and I don't propose to add to that here.

Suffice it to say that many of the Confederate commanders, including Heth, do seem to have acted as if there was no cavalry available for reconnaissance. We can see this in his report where he observes:

It may not be improper to remark that at this time--9 o'clock on the morning of July 1--I was ignorant what force was at or near Gettysburg, and supposed it consisted of cavalry, most probably supported by a brigade or two of infantry.

He then goes on to give his account of the battle that followed. From that account, it is clear that Heth's mission on 1 July was essentially what we would now call a reconnaissance in force to determine whether the soldiers they had seen in the town were harmless 'home guard' troops or elements of the Army of the Potomac.

Of course, an element of caution is appropriate. Everything that was written after Gettysburg by those involved in making the decisions was in the context of the Confederate defeat, and attempts to avoid / deflect blame.

Shoes

It is clear that one major objective for Heth, and indeed of the invasion as a whole, had been acquiring supplies for the Confederate army. His report of 13 September 1863 concludes with the following:

I take this occasion to mention the energy displayed by my chief quartermaster (Maj. A. W. Vick) and his assistants in collecting transportation for the division when in Pennsylvania, the division having a limited supply when it crossed the Potomac; also to Major [P. C.] Hungerford, chief commissary of subsistence, and his assistants, for their activity in procuring supplies.

It is also true to say that Heth's men - in common with much of the Army of Northern Virginia - were short of shoes. However, it is probably going too far to suggest that the shoes were the _proximate cause for confederate interest in Gettysburg that day.

Shoes were were certainly an important goal (as shown by the parenthetical comment in Heth's report), but they were far from being the only one.

One of the things that makes Shelby Foote's The Civil War: A Narrative! such a compelling read (quite apart from the research that underpins it) is the fact that Foote is an immensely skilled storyteller.

As Brendan Wolfe wrote in his article Shoes at Gettysburg on Encyclopedia Virginia:

"... "shoes especially" represents the perfect detail, quickly translating abstract historical forces into blisters on aching feet and the smell of new shoe leather. "

He went on to observe:

That it started by accident, over something so "pedestrian" as shoes, is too perfect for writers to ignore. Shelby Foote certainly did not, crafting a scene in The Civil War: A Narrative (1963) in which A. P. Hill airily dismissed the possibility that the Army of the Potomac was in Gettysburg:

In Foote's dialogue, Heth was quick to take him up on that. "If there is no objection," he said, "I will take my division tomorrow and go to Gettysburg and get those shoes."

"None in the world," Hill responded.

In fact, as we saw above, Heth's mission on 1 July was actually a reconnaissance in force to determine the actual composition of Union forces in Gettysburg. That mission resulted in a contact engagement from which neither side was able (or willing) to disengage.