"To embrace the idea" means to accept and welcome a particular concept, belief, or suggestion wholeheartedly, and to fully support or adopt it. Full definition
If you haven't fully embraced the idea of using social media for your job search, let me help. (careersherpa.net)
It is common for babies to not embrace the idea of solid food at the first time. (newkidscenter.com)
If we looked at it that way, we would probably feel very different in those low moments, because we could really embrace the idea that something great must be around the corner. (entrepreneur.com)