A new address has no sending history, and receiving providers treat unknown addresses cautiously.
WHY WARMING MATTERS
Suddenly sending a large volume from an address with no history looks exactly like a spam run. Mail may be throttled, filtered or rejected for weeks.
HOW TO WARM IT
Start with low volumes of mail to recipients who expect it and will engage with it. Increase gradually over several weeks rather than all at once. Prioritise transactional mail, which recipients open, over bulk mail, which they may not. Keep bounce rates low by cleaning invalid addresses before sending. Avoid sending anything that will attract spam complaints during this period.
WHAT TO HAVE IN PLACE FIRST
Correct SPF, DKIM and DMARC Reverse DNS matching your mail hostname A From address on your own domain
THE HONEST POSITION
If you cannot commit to a gradual ramp, a new dedicated IP will likely deliver worse than the shared address you left. For most senders, that is a reason to stay on shared, or to use a dedicated sending provider that manages reputation for you.