數+量 counts how many (三本書 = three books); 第 + number names which one in line (第三本書 = the third book). Drop 第 and the rank collapses back to a quantity; add 第 and 三 stops meaning 'three of them' and starts meaning 'the third'.
✗ 一次 (for 'the first time') → ✓ 第一次
✗ 第三的書 → ✓ 第三本書
English builds ordinals by changing the word's ending (three → third); Chinese keeps the number whole and prefixes 第, so learners reach for a suffix or drop 第 entirely.