Is it possible to foster a culture of continuous learning in a whole team?

Yes
it is absolutely possible to foster a culture of continuous learning in a whole team.

Creating a culture of continuous learning can lead to numerous benefits, such as increased innovation, improved productivity, enhanced problem-solving abilities, and higher employee engagement and satisfaction.

I believe it’s always key for people to understand WIFIM. ( What’s In It For Me)

Culture is emergent. Ensuring the incentives for your team align with a continuous learning culture and that those are reinforced with each action going forward, is the main way you can cause this emergent behavior to manifest. Are people rewarded for learning new skills, discovering issues and finding creative solutions? Do you reward for the actions you want from this culture in the form of recognition, promotion, experiences or monetarily? Is it ok to fail within the organization? Are there protections in place to create safety for said failure, both de-risking for the organization and individual? Do you have good data to inform, not just infer? 

As a start, learning needs to be a core expectation for the team.

I have found that many tech folks do a lot of self-learning, but don't necessarily make the connection. Any research or work to "figure out" an effort is one thing to reframe for folks.

A daily question "What did you learn today?"

In general, reframe learning as part of "work" and not something that is extra or separate from their regular duties.

Of course. You can provide opportunities for professional growth, a structure/path for learning and development, and motivation. 

Yes, it is absolutely possible and beneficial to foster a culture of continuous learning within an entire team. Here are some strategies to achieve this:
- Lead by Example
- Provide Learning Opportunities
- Create a Safe Environment
- Recognize and Reward Learning
- Integrate Learning into Regular Work
- Encourage Knowledge Sharing
- Provide Resources and Tools