can protestants have their sins forgiven since they do not confess to a priest?
As the poster above pointed out, God can forgive anyone at any time for any or all of their sins, by a free act of His grace. Given what the Church teaches about contrition or acts of contrition, it’s hard to imagine a Protestant could not abhor their sins or sinful ways (and we are assuming they have been sinning, even mortally), implore God’s mercy and forgiveness for their sins, and that to the point where it could be supposed that if he or she were aware of the need for Confession and Reconciliation, they certainly would (or would have) confess(ed) and done everything Reconciliation usually requires (e.g. penance). Under such circumstances I imagine we would have to believe or assume that their sins were indeed forgiven by God, though again it would be left up to God: that is why the sacrament of Confession and Reconciliation is such a great gift and act of mercy to the Church: it allows Christians a true and reasonable certainty that we have indeed been forgiven by God for our sins and have been restored to His grace and fellowship.
I think many of David’s Psalms help give us an idea of the kind of sorrow and repentance and abhorrence for sins that is appropriate for believers and expresses a true conversion (and softening, as a kind of fruit of repentance) of the heart. Of course, I think invincible ignorance could apply to some sins a Protestant Christian may have committed but, again, in ignorancel and again, if it could be said that had he or she known those were sins, and particularly mortal sins, they would have ceased and abhorred such acts (or inaction, as it might happen), then I think we can be reasonably confident that their sins would also have been forgiven them by God. But again, however, God is always free to forgive or not to forgive sins and as far as I know the only time we can have certainty about the forgiveness of sins revolves around baptism and the Sacrament of Reconciliation, which includes contrition and penance.
See, for example, the Catholic Encyclopedia on Contrition and the Sacrament of Penance. You could also look up what the Catechism says about the forgiveness of sins - but remember that sometimes it might be assumed the person is a Christian (i.e. baptized) and further a Catholic and the sin is post-baptismal but other times perhaps non-Catholic Christians or even non-Christians, which changes things.
God bless.