I wouldn’t say that Chinese verbs have no tense so much as that they are uninflected and that tense is marked with particles (which admittedly do not cause difficulties with irregular infexions).
However, the verbs themselves don't have tense. So these sentences can be identical: "I will walk home, then I will eat a cake" and "I walked home, then I ate a cake".
The overall timeframe can be given by a larger context: "Once my shift is over, I ..." / "I drank too much yesterday, that's all I remember: ".
It's simply not possible in English because every verb has a grammar tense built into it.