We find incepi, meaning "I began" in Medieval latin.
In the Classical period, "I began" is normally expressed by COEPI. The perfect incepi is not used (so far as I know) in order to mean simply "to begin" (as in "the rain begins to fall").
See for example
VARRO, De lingua Latina, X, 9
Quem locum, quod est difficilis, qui de his rebus scripserunt aut vitaverunt aut inceperunt neque adsequi potuerunt.
« And just because this topic is difficult, those who have written of these subjects either have avoided it or have begun it without being able to complete their treatment of it. » (Translated by Roland G. Kent, Loeb)
Here, the verb means rather "to take in hand". It is about a deliberate undertaking, not simply the beginning of something.
Plautus, Trinummus, 465-470
male quod mulier facere incepit, nisi <id> efficere perpetrat, 465
id illi morbo, id illi seniost, ea illi miserae miseriast;
bene si facere incepit, eius rei nimis cito odium percipit.
nimis quam paucae sunt defessae, male quae facere occeperunt,
nimisque paucae efficiunt, si quid facere occeperunt bene:
mulieri nimio male facere levius onus est quam bene. 470
« A thing that a woman attempts to do in fraud, unless she is perfect in carrying it out, that same is as bad as disease to her, that same is as bad as old age to her, that to her, wretched creature, is wretchedness: if she begins to do what's right, soon does weariness of it overtake her. How very few are tired who have commenced to do what's wrong; how very few carry it out, if they have commenced to do anything aright. To a female it is a much less burden to do bad than good. » (Translated by Henry Thomas Riley [Perseus])
Here incepit = "has undertaken". It is more vivid so.
Note : needless to say, I don't agree with the underlying machismo.