Within Teamwork, you can upload files directly to your integrated storage apps such as Dropbox and Google Drive.
In the Files area of your project, click the File Integrations button in the top right to select the storage integration you want to use.
In the integration modal, you will have an option to upload in the top right corner.
When you click Upload, you will be prompted to choose a file and it will be added to your selected folder.
Once a file has been uploaded, you can use the checkbox on the left of the file name to select the file and click Link-in Selected Files to link it to your project.
For more information, see: Linking Files from Integrated Storage Accounts to Your Project