Best method to impute time series with missing values in early years when time series will be differenced

Question

I am building a VARMAX model with endogenous and exogenous time series variables. The dataset consists of years 1950-2019 for all time series variables except one exogenous variable which was not available until 1982. The time series are not stationary and require differencing. Therefore, it's useless to impute the missing values using techniques like setting them equal to the mean or using the last known observation because once I difference the series all of the imputed values will be equal to 0. I'm looking for recommendations for the best imputation technique in this case?