I would not enter expenses related to the moving expense deduction if I did not have the receipts and/or invoices to backup my deduction. If IRS contacted you for documentation related to the moving expense deduction, and you had no documentation to give them, you would be assessed tax, penalties, and interest.
If you used a moving company or rented a truck you can contact the company to request a receipt. Did you pay for any of the expenses by credit card? You may be able to use your credit card statements to help re-create your moving expenses.
https://turbotax.intuit.com/tax-tips/jobs-and-career/irs-moving-expense-deductions/L5podfG5I
