The Greeks took their alphabet from the Phoenicians. In that script the letters clearly have a pictorial value, stemming from their hieroglyphic origin, Thus Aleph was an ox head; Beth, a house; and Gimel, a throwing stick (later a camel). All of these things were important to powerful people in those lands, individuals who could afford to subsidize scribes.
Why though was Aleph the first? In many early cultures, cattle were a trope for wealth. So in Latin we have pecus, the origin of our “pecuniary.” The English word “fee” is a cognate of the German noun Vieh, meaning cattle. This consideration suggests that placing the sign for cattle first would be the equivalent of our starting an alphabet with a $ sign.