Worked with Epicor in a similar situation in a past life. There are either consultants or Epicor itself doing the upgrade, it won't just upgrade. Are you on their cloud offering? Most of your internal teams should have already validated that they are good to go in a test environment. If you can list some kind of contact I'd be happy to walk you through some things.

Step one that I always told my teams. When something comes in on fire, step one after entering the ticket/basic information is getting a cup of coffee. This give you a second to calm down, start thinking about the issue instead of reacting to the issue. You are going to get frantic floor workers coming in saying 'XYZ gehimazoid isn't working'. If you catch their panic, then run to the floor, your hit. Gather info. Send them on their way and tell them you will come look into it shortly. Get a cup of coffee. Come back and without them staring over your shoulder Google 'WTF is a gehimazoid' or HOPEFULLY look it up in your internal IT knowledgebase.

Find out who the leads on the floor are going to be that first day. Try to set things up where they will come report issues to you, so you don't have 100 floor workers coming to you panicked. They are a huge line of breathing room for you and they are hopefully more understanding of the situation.

Immediately after upgrade I would prioritize that the factory floor can enter work into MES. You don't want 150 people and millions of dollars in machines sitting idle. So can they get to their work orders, can they get to their MBOMs, can they get to MES if you are using it.

I would prioritize that departments can run their key reports. Not every report, key ones.

Identify if you have a report writer, and what their level of capability is. They are going to be your best friend during this as reports are going to be one of the most visible potential issues. If you don't have report writers, you are going to have someone in finance who needed custom reports and learned it all on their own. See if you can find them and if they are friendly.

The system should be running a Microsoft SQL Server backend. If it is on Progress, than you need to scream tilt and ask for resources. Progress isn't hard or bad, but it is just niche enough that there aren't a lot of helpful resources.

Reports should be Epicors implementation of SSRS. Do you understand how SSRS reports run? There can be custom reports, so identify what departments use custom reports.

You will need to ensure the following minimal capabilities are working after the upgrade. Try to find out who is using custom reports to do any of this ahead of time. Once minimal functionality is working you can move on to the next level of fires.

Finance:
They may have custom Crystal Reports because well, finance often can do what they want, so yeah. Don't yell at them like you would some production planner using custom Excel hooked into the system.

Production Planning:
They use the system to generate future jobs/work orders. They will need to keep the floor fed with work orders so make sure they can print them along with MBOMs etc. While scheduling jobs out in the future is important, first focus on the floor so that current production doesn't stop. So that is picklists, work orders, MBOMs, etc.

Stockroom:
Picklists
Non reporting: Entry into MES if you use MES

Factory Floor:
Jobs.
MBOMs.
Non reporting: Entry into MES if you use MES

Buyers:
POs

Shipping/Receiving:
Packslips