How to bring today"s date to the process variables?

It also seems you want to default to today's date as well.

I will add on to Bob's answer with the following code. Note the updated "value" field for the dateField. 

{
  a!dateField(
    label: "Order Submission Date",
    value: if(
      isnull(ri!OrderSubmissionDate),
      fn!today(),
      ri!OrderSubmissionDate
    ),
    saveInto: ri!OrderSubmissionDate,
    required: true
  ),
  a!buttonLayout(
    primaryButtons: {
      a!buttonWidget(
        label: "Submit",
        saveInto: {
          a!save(
            ri!OrderSubmissionDate,
            if(
              isnull(ri!OrderSubmissionDate),
              fn!today(),
              ri!OrderSubmissionDate
            )
          )
        },
        submit: true
      )
    }
  )
}

It also seems you want to default to today's date as well.

I will add on to Bob's answer with the following code. Note the updated "value" field for the dateField. 

{
  a!dateField(
    label: "Order Submission Date",
    value: if(
      isnull(ri!OrderSubmissionDate),
      fn!today(),
      ri!OrderSubmissionDate
    ),
    saveInto: ri!OrderSubmissionDate,
    required: true
  ),
  a!buttonLayout(
    primaryButtons: {
      a!buttonWidget(
        label: "Submit",
        saveInto: {
          a!save(
            ri!OrderSubmissionDate,
            if(
              isnull(ri!OrderSubmissionDate),
              fn!today(),
              ri!OrderSubmissionDate
            )
          )
        },
        submit: true
      )
    }
  )
}