English Translation
To our surprise, our son has suddenly shot up recently.
Unnatural collocation. すくすく means “to grow rapidly and in a favorable way”. すくすく成長する and すくすく育つ sound natural. But we don’t say すくすく背が伸びる. Furthermore, 背がのびてきた should be replaced with 背が伸びてきた in Kanji.
If you want to stick to the phrase 背が伸びる, its preceding onomatopoeia should be グングン in Katakana or ぐんぐん in Hiragana.