I think the question might need reframing. The Buddha's Dhamma is of two types ([MN 117](https://www.accesstoinsight.org/tipitaka/mn/mn.117.than.html)): 

1. mundane/pertaining to merit & morality 
2. supramundane/transcendent 

For me, the question is: "*Did the Buddha ever offer supramundane teachings without being asked to?*"

The account of the First Sermon in the [Vinaya](https://suttacentral.net/pli-tv-kd1/en/brahmali?layout=plain&reference=none&notes=asterisk&highlight=false&script=latin) gives the impression the Buddha was pushy & offered to teach without being asked: 

> The Buddha said to the group of five monks, “Monks, don’t address the Buddha by name or as ‘friend’. Listen, I’m perfected and fully awakened. I have discovered the deathless. I will instruct you and teach you the Truth. When you practice as instructed, in this very life you will soon realize with your own insight the supreme goal of the spiritual life for which gentlemen rightly go forth into homelessness.
> 
> The Buddha was able to persuade the group of five monks. They then
> listened to the Buddha, paid careful attention, and applied their
> minds to understand.