Is there any way to summit khatadin the first week of april?

Yeah what Erik said lol

You can summit at any time of year. If the roads are not yet open for the summer, though, you'll have to walk in along the roads and either do the peak in one day, or reserve space at a cabin/lean-to or otherwise camp somewhere along the way. The BSP website has good info for visiting the park in both winter and non-winter seasons.