To determine the first MONTH of each year (timescale set to month), I would recommend using a boolean formatted line with a formula along the lines of MONTH(ITEM(Time)) = 1.
To determine the first WEEK of each year (timescale set to week), it is a little tougher. I would translate the week into a year so the line item would say FY18 for every week until reaching FY19 and then say FY19 for the 52 weeks. Then, you could have another line item that says if Year line item > Previous(year line item) then TRUE (i.e. would work out to say IF FY19 > FY18 THEN TRUE).
This will check the first period matching the dimension of the target module and the Year time properties.
As Anaplan does not have a native week time scale that can be used as a time dimension you will need to map the first week into the year manually in your year time settings module. Then instead of referencing Time with an ITEM function you will reference the weeks list.