I need to merge ~8k of .asc files into one big one. To convert each one into a raster first would take forever .. is there a possibility to convert multiple ascii files to raster in ArcGIS?
ASCII is an Esri format, you don't need to convert it first. That is assuming the files called .asc are really Esri ASCII Grid format and not just some other text raster format (like X,Y,Z).
Open one in Notepad++ (or your other favorite text editor) and see that it conforms to this format:
NCOLS xxx NROWS xxx XLLCENTER xxx | XLLCORNER xxx YLLCENTER xxx | YLLCORNER xxx CELLSIZE xxx NODATA_VALUE xxx row 1 row 2 ... row n
Now assuming that it does, create a File Geodatabase and then in it create a Mosaic Dataset (you indicated ArcGis 10.3, this is new at 10.0) by right clicking in the database and select on the context menu new::Mosaic Dataset, fill in the blanks and hit OK.
Now you have an empty dataset right click and select add rasters then select all your .asc files. This does not convert your files, only linking, this operation should be fairly fast.
For performance it's a good idea to build pyramids; only the links and pyramids are stored in the database, the rasters are unchanged (so don't move or delete them). You can use the mosaic dataset 'as is' in ArcMap or using a tool like Copy Raster you can export it to a single image (like Img or GeoTiff/BigTiff).