Yes, you can check with your bank if they can provide you CSV files of your bank transactions for several years. Then, import them to QuickBooks Online. I'd be glad to walk you through the steps.
Once you've got the CSV files, you can go to the Banking menu and manually upload the file from there. Here's how:
From the left menu, click Banking.
Select the appropriate bank account.
Click the drop-down arrow beside Update and select File upload.
Select Browse, then look for the file and click on it.
Follow the on-screen instruction to upload the file.
If your bank doesn't support CSV files, you can use Quicken (QFX), QuickBooks Online (QBO), or Microsoft Money (OFX) files to import. You can check out these articles for the detailed steps and information: