I have a level one assault charge that was taken place in 2004 would I be able to cross the USA border without a pardon?

You can try to cross the US border with your assault offence as the Americans do random criminal checks. However, you may be denied entry to the US if they do a criminal check and see that you have this offence. Usually the Americans are concerned with more serious offences than an assault, however they can still deny you entry. Once your pardon is granted and the assault no longer shows up on the RCMP file then you will be safe to travel without worry. If you are denied entry to the US before your pardon is granted then the pardon is no longer valid and then you will need a US Entry Waiver or I-192 to return to the US which is a lot more expensive and complicated process.