Yes, you should be able to delete the unused partition and grow the other partition.
However, since the partition you want to get rid of is ahead of (instead of after) the one you want to keep, I do not believe you can do it with Windows' built-in Disk Management tools. You will need to use a 3rd party partitioning tool to delete the first partition, then resize (and move) the existing partition down to the start of the disk.
I generally use gparted
for stuff like this. However, it is geared more towards Linux users, and does not handle all types of Windows partitions (e.g. it can't handle Windows "Dynamic Disk" partitions).
Any time you manipulate partitions (and especially if you are moving/resizing them), there is some risk of data loss. To ensure that no data is lost you need to make a backup of the files in the existing partition to another disk or external media before proceeding.
It may be easier to just back up all of the data, reformat the disk with a single partition, and copy all of the data back.
It sounds like this is a data disk, so there is no need to mess around with an OS partition.