If you apply for studies at a university or polytechnic through the joint application system, you will have to consider the application deadlines as seen below.
Application deadlines for studies at Polytechnics in Finland
For study programs conducted in English, the usual application period starts approximately 6 months in advance of the beginning of the program. For example, if your program starts in autumn, the deadlines will most likely be by February. Please note that you must submit all supporting documentation before the deadline expires in order for your application to be considered. About 2 months after the deadlines expires, your university of applied sciences/polytechnic will inform you whether you have been admitted to the program you applied for. You will have to confirm you accept your study place after that.
Application deadlines for studies at Universities in Finland
The application period begins around November and runs through February - April depending on the study program. Please, check at the institution website the specific deadline for the course of your choice.
Source: University Admissions Finland (the centralized application service established by Finnish universities).