Before I move into the question there are no spoilers here.

I am about to embark on a lengthy D&D adventure with some new players that will start with the Lost Mine of Phandelver (LMoP) and then continue into Curse of Strahd (CoS). I envision LMoP will take 4-5 sessions (it may be slow moving with the new player) and then we will move on to CoS after that.

I have already run LMoP before and some other shorter adventures like A Wild Sheep Chase and The Low Crater, but I am very intimidated at the thought of running a longer adventure like CoS. I know the first step is to read the book cover to cover, but how do I prep for a pre-canned adventure of this size that also has a sandbox portion?

There is no way I can possibly memorize everything in CoS and I don't want it to be railroady. The sandbox element of CoS is part of its greatness. How do experienced DMs prep for an adventure this size?

Ask "What would you like to do next session?"

This is a question I ask my players at the end of a session where the next steps are quite vague. If they're in the middle of a dungeon crawl when we finish for the evening, I have a very solid idea of what they're going to be doing next time we sit at the table.

However, if you're playing a sandbox portion of the adventure, make sure your players are communicating with you what their intentions are. It's not railroading to prepare what's in Town1 if the player's specifically state they want to check out Town1 next time they play.

All DMs know that players are unpredictable though and their plans can change, which is fine. You've already stated that you know to read the whole book (or at least the main parts), so this is where your knowledge of the source material and improvisation skills come into play. I always have some extra locations/encounters/plot hooks stored away for this sort of scenario.

So sometimes the unknown is unavoidable. But a little bit of communication with your players would definitely help.

Prep one session around your players

After a few sessions of LMoP, you will have a good idea of how far your party can get in a day. Even though CoS is somewhat sandboxy, there's no way they're going to end up in

Vallaki, Kresk, The Winery, the Amber Temple, or the castle

in the first session. Travel takes time as well, and you can throw some combat encounters at them along the way to cities that you haven't fully prepped to finish out the rest of a session. Both inside and outside the cities, there's a hierarchy of things that do not need to be fully ready to go as soon as the characters reach the city.

Choose your session end point carefully

If your players are in a particular city with multiple things to do and see, and they choose a path you didn't anticipate, leave them on a cliffhanger. Obviously this doesn't work if you literally just sat down, but if you choose your end point such that a particular action on their part is unresolved, you know what they are going to do first next time. End the session when they, exhausted after a rough day of travel, finally see the gates of the next location. You then know that they will need an intro to a particular city at the start of the next session.

Steal

Many other DM's have run CoS and written it up, on blogs of their own, reddit, and here. They've all fleshed various things out, emphasized the bits they or their groups found important or compelling, and can help direct your prep a little.

Lie

Don't give the players a reason to leave

Vallaki or Kresk

before you've fully prepared the next area. You should know where they are likely to go next, based on the hooks you've provided, and maybe all their investigative efforts until you've prepped what comes next point to things inside the city, or the questgivers could indicate that what they are asking for is a very dangerous endeavor. Or,

the Baron catches them on the way out and directly asks them to participate in that days festival, and we all know how much the Baron loves festivals. I had a festival ready to go that required the players participation and had to use it to keep them in town for the remainder of the session.

Cheat

You're the DM. There's so many tools at your disposal to keep them away from parts of the adventure you're not ready for them to experience. Remember,

Strahd has his eyes and ears everywhere, and knows the players movements even before they do sometimes. If they try to go to the castle, Strahd could send them a message, or ambush them. The woods are fraught with peril and the Vistani and wolves are under Strahd's influence.