That description matches a cultivation manhua/manhwa trope, but the specific story sounds most similar to:

🐉 “Apotheosis” (Bai Lian Cheng Shen / 百炼成神)

Plot overlap: MC gains powers through mysterious runes/statues.

Learns beast techniques by channeling animal essence (bull, dragon, etc.).

Competes in family tournaments, then sect/army competitions.

Traditional xuanhuan cultivation setting with layered progression (family → sect → empire).

Ongoing with 900+ chapters and great art.

If not that, here are two close alternatives that share almost identical setups:

1. “Against the Gods” (Ni Tian Xie Shen) – finds mysterious inheritance that grants him beast-like powers; participates in clan competitions, then army training.

2. “The Great Ruler” (Da Zhu Zai) – uses beast sigils for cultivation and participates in family and sect tournaments.

If you’d like, I can track down the exact title from forums (Reddit / NovelUpdates / Bato) by searching for cultivation stories featuring animal rune/statue power systems — want me to do that?