By the rules, yes
From the CRB (emphasis mine):
Each item has an item level, which represents the item’s complexity and any magic used in its construction. Simpler items with a lower level are easier to construct, and you can’t Craft items that have a higher level than your own (page 243). If an item’s level isn’t listed, its level is 0. While characters can use items of any level, GMs should keep in mind that allowing characters access to items far above their current level may have a negative impact on the game.
So that's explicit: a lvl 1 character can use a lvl 4 item if they get one.
On top of those rules, there is an advice, targeted to GMs: the system is balanced by assuming characters have access to items of a level lower or equal to their and thus changing this in your game may have bad consequences for your game
How affordable is a striking rune?
65gp is a lot of money for lvl 1 adventurers. Unless you are lenient with player's inventories, it looks hard to me to save more than 10gp once you have bought the essentials (clothes, one melee weapon, one ranged weapon, a backpack, a few rations, a bedroll...).
Truly, to have this at lvl 1 means you have a larger group than average and your players deprived their characters from other items they may need.
Actually, if you follow the guidelines about treasure per level, by the end of lvl 3 the whole party should have gained around 120gp in spendable coins, which is enough to buy one striking rune but would still require that two members of the group put their share of the loot together
What does this rune do exactly?
It adds a damage dice. It doesn't add +1 to hit (for this you would need the +1 rune, that would add 35gp to the cost). Ok, but is that big?
Assuming you play with the higher dice possible, you would roughly jump your damages on a hit from 1d12+4 (10.5 avg) to 2d12+4 (17 avg). Not bad at all.
Assuming you play a Fighter (probably the class that will benefit the most from this rune), you usually hit most of your non-boss opponents at those levels with an 8, and crit with an 18. This makes an average damage of 16*17/20=13.6 on the first attack with the rune. (8.4 without the rune)
On the second attack a 13 is needed to hit, and only a nat 20 crits. It makes for an average of 9*17/20=7.65 damages. (4.725 without the rune)
This is great, indeed, adding more than 5 damages on your first attack is huge, but a lvl 2 creature has 30hp on average, so you still usually won't finish it in one turn. On the scale of a whole encounter, even with this powerful rune, this Fighter isn't going to break the encounters on their knee: they still need the rest of the party. And if the rest of the party has no stuff at all they are not going to be able to do their part.
Worse, when this Fighter will get downed (it always happen to frontliners in this level range, and will definitely happen if they are not wearing armor as they didn't have money to buy it), the rest of the group will have lost access to their only asset.
For all these reasons, I don't think a group with early access to this item would be stronger than a normally equipped one.
How else can it have a negative impact on the game?
This is more obvious to me. Usually, players play Pathfinder as a team of equals who each bring their own talent to the party and each can have their moment to shine. Playing a useless follower of a very powerful warrior isn't a fantasy most people share, and at least around a Pathfinder table this is not the assumption.
For this reason I wouldn't allow pooling starting money before the game. Each player must be able to afford their basic stuff so that they can operate in the team without being incited to give it to someone else.
Later, once the party has earned 65gp as a group and has it available to spend, maybe it will be time for a striking rune, but by this time they should have gathered other magic items and tried them out and may have found that they need other items in priority.