Words that end with さ are often words that have taken the adjective form (in this case 大きい) of the word and turned into words that describe what the adjective form is doing, if that makes sense. So 大きい (big) goes to 大きさ, and the word that describes what "big" describes is the word size.

When a vocab has okurigana (hiragana attached to the kanji) it is probably going to be the kun'yomi reading. Since you learned the on'yomi reading with the kanji 大, we'll have to use a mnemonic to remember this word.

When you saw the size of (pick something surprising), you said "おお *#$@!" Really imagine something surprising. Say the おお part out loud, as well. Think about the size of whatever you're looking at, too, and how big it is.