Perhaps one of the most challenging things about learning Japanese is that it does not have an alphabet – but it appears to have an alphabet. So we, as English speakers, try to overlay what we know about alphabets onto Japanese, and then it simply doesn’t work.
Japanese, instead, has syllabaries – which are very different animals. They are more like a grid than anything else. There is no set order – in fact, any order that we put them into when we learn Japanese is based upon the romaji order – a b c, etc. They don’t even have names, like romaji characters do – they are basically named after the sounds they make.
And the syllabaries aren’t an alphabet in another important way – they were created from kanji as a simplified way of representing syllable sounds. The true alphabet in Japanese is in the kanji, as pointed out by kanji damage. This alphabet is in the form of radicals, many of which were actually abstracted out into the syllabaries. There does not seem to be an order there, either, but those symbols are used to build up words in the form of kanji.
But not only are we not taught/do not recognize that, we even come into the whole deal thinking that kanji that have the same radicals are related to each other. But they’re not, in the same way that the word “add” is not related to the word “ade”, even though they have two letters in common.
So while memorizing the syllabaries is absolutely necessary to learn Japanese, it’s not at all learning the alphabet in the same way that we learn the alphabet in English as children. It’s learning the phonetic building blocks of Japanese. The letters of the romaji alphabet are not the phonetic building blocks of English language. We have special, not widely known characters for that purpose.
So in learning the Japanese syllabaries, you are learning the sounds. The letters (which are not related to the sounds in any but a superficial way) are actually the kanji radicals.
Basically, unlearn everything you knew when learning English. It really doesn’t apply – at least not in anywhere near the same way. That’s the only way, I think, one can start understanding Japanese.