Should I check it first thing in the morning to see if I have any urgent things to work on or should I try and continue working on whatever project I was working on the previous day and try and crank out that couple hours of productive work above all else?
I feel strongly that you should not check email first thing in the morning. If something is truly urgent and requires your attention, someone will ping you about it.
Come into each morning with a clear idea of what you want to focus on. The morning hours are critical for deep work -- make them proactive rather than reactive.
(BTW, I feel the same about almost all other notifications other than DMs. Don't check Twitter/Instagram/any other app until you've made progress on your top priority)
You may also benefit from the masterclass about time management: https://www.jointaro.com/lesson/rnX9EKpzc43TgGW9MozG/how-to-manage-your-time-optimally-in-tech-and-achieve-more-results-792021/
What Rahul said, plus trial and error on your email timing within the day.
Review all the meetings you have in the morning. After subtracting the meeting time, consider what are the reasonable goals to achieve within the day. Know what you want to achieve by yourself, e.g. coding, writing documents, etc. Know what you want to achieve when interacting with others, e.g. getting alignment in this meeting, delivering some touch feedback in that 1:1, etc.
Keep information consumption in polling mode instead of pushing mode if you have the power to do that. (It really depends on the company's culture and your positional power.) There's no one-size-fits-all solution. Trial and error to see how far you can push the envelope -- how unresponsive other people can tolerate you. Of course, you need to set expectations with the people you work with, again and again. I used to tell people "don't expect me to attend a same-day meeting if you send the calendar invite late". (I was a manager at the time. I needed tight control over who I had to meet ASAP and whose meeting I could postpone.)
Gradually you will figure it out. You will see a pattern of when the people in your company usually make communication with what you care about each day.