How can I import all of my existing emails from a PST file?

If you want to import all existing emails from a PST file, the right method depends on where you want those emails to be imported. It is important for a large mailbox to keep the folder hierarchy, attachments and message properties rather than exporting individual emails. 

In case the destination requires a different email format, then you may try

for bulk PST conversion. It can process single PST or multiple PST files in a folder and export the mailbox data to MBOX, EML, EMLX, MSG, NSF, TGZ, HTML, MHTML, PDF and IMAP file formats. Conversion preserves folder and subfolder hierarchy, email properties and attachments. 

For a complete mailbox, batch processing is useful because all selected PST data can be handled together. The Date Range filter can also be left unused when the intention is to process the entire PST rather than a specific period. 

Before importing the complete mailbox, test a sample PST and verify the resulting folder structure and attachments.