Reibun
、。

It goes without saying that at that moment, something like a friendship transcending the master-disciple bond was budding between the two of them.

Literal

That time, two-persons [gen-の] between [at-に] master-disciple [obj-を] surpassed friendship [like-のような] thing [subject-が] sprouted thing [topic-は] say-until-not.

言うまでもない is a fixed expression — 'it goes without saying / it needn't be said.' のような ('like / something like') is the attributive form of the simile marker のように, modifying もの. 師弟 ('master and disciple') + 越えた ('surpassed, went beyond') makes a relative clause modifying 友情 — 'a friendship that went beyond the master-disciple relationship.' 芽生える ('to bud, to sprout') is a metaphor from plant growth, extended here to feelings. The two こと-nominalizations (友情のようなものが芽生えた事) bundle the whole clause up as a discussable topic.