Here are some actions that you can consider taking now:
Designate a Y2038 Compliance Officer to serve as the company focal point for Y2038 compliance. This position may or may not be full-time depending on the size of the company. The person in this position could, for example, report to a senior officer, and also chair a committee comprised of directors/managers or representatives from every major division in the company. The person in this position will be responsible for keeping documentation on compliance findings and status.
Implement corporate policies for Y2038 compliance. For example, a policy may require that all new projects be designed, tested, and maintained for Y2038 compliance if at all possible. The policy can further require that exceptions be formally documented and approved, thereby enabling them to be tracked and addressed sometime later.
Start assessing your company’s level of exposure to Y2038. This should include all digital systems used or produced by your company, from the largest business system to the smallest embedded system. It should also include all databases and storage systems, third-party and developed system and application software, and any custom network protocols. When issues are found with third-party products, you should contact those vendors and request that they update their products to be compliant.
Budget for Y2038. The above actions cannot happen without a financial commitment from management. Postponing these actions also has a cost, likely much higher than you expect. The cost is not just money… it is also time (since issues will take longer to fix later) and employee satisfaction (since developers generally want to work on new things, not on date issues in old systems). Budgeting now will save money in the long run.