How to access the params in every incoming requests?

I got a middleware dedicated to checking if the record with recordId existed in my MongoDB database.
Now I wish every single request to go through this middleware with the inspiration from DRY. So I created an application-level middleware:
app.use(checkRecordsExistence)

The middleware checkRecordsExistence needs to access all param list in order to check the existence of relevant records and store them in req object for further use.

However req.params always returns {}. What is the way forward? I don’t want to add it in the router-level middlewares, because it is not clean, I worship DRY.

Here is my detailed implementation.

const checkRecordsExistence = asyncHandler(async (req, res, next) => {
    const { params } = req;
    for (const key in params) {
        if (Object.hasOwnProperty.call(params, key)) {
            // Only check params corresponding to Object Id
            if (key.endsWith('Id')) {
                // Remove the "Id" suffix from the param name
                const modelNameLower = key.slice(0, -2);
                const modelName = modelNameLower.charAt(0).toUpperCase() + modelNameLower.slice(1);

                const Model = mongoose.model(modelName);
                const recordId = params[key];
                const record = await Model.findById(recordId);
                if (!record) {
                    return next(new ErrorResponse(
                        new Error(message.notFound(modelName)),
                        404
                    ));
                }
                // Attach the found record to the request object for further use
                // <=> req._class = await Class.findById(classId)
                req[`_${modelNameLower}`] = record;
                console.log(typeof(record));
            }
        }
    }
    next();
});

I can get it going well by putting the middleware in every single router-level route. But it is not clean.