I wrote the below before your lawyer's response here. Listen to your lawyer, try to avoid taking major actions without his/her advice. Our common sense and thoughts of being "nice" is not the legal way, an accumulation of decades of laws and case law and procedures and policies and... .whatnot.
On the other hand, if you do pay something then do not go overboard. If you overpay you will certainly not get a credit or refund! Very likely a court will IGNORE prior payments that were not ordered or view them as GIFTS. I recall when I filed for divorce it took 2 months to get a hearing and then I was ordered to pay retroactive Child Support. You can try to mark on the checks that they are for "child support" but we can't assure you that those unordered payments will be taken into account.
They will set child support when issuing a temp order. Right now they're just getting a handle on what the the issues are? For example, if you're not granted any parenting time in the current status it is possible that you have Domestic Violence, child abuse, child endangerment or child neglect allegations pending that are currently being investigated?
This is a truism around here... .
The parent who is behaving poorly seldom gets consequences and the parent who is behaving well seldom gets credit. Ponder that for how it fits each of you. If she's made allegations and they're discounted, it won't make her look all that bad to the court. If you "gift", for example, $100 per week toward Child Support and later the court sets an amount higher, it won't make you look all that bad to the court (and you won't have looked that bad either).
Remember, court can choose to IGNORE unordered payments, later viewing them as GIFTS. What does your lawyer recommend?
Should I give her financial support in mean time?
Oh, I didn't quite answer that. Well, in a manner I did. When comparing the circumstances of children and spouses, children always get the priority with agencies and courts. After all, children are minors not expected to be self-sufficient, spouses are adults and they're expected to know how to navigate life. That's why I suggested everything you provide to be cast as "child support" and not "spousal support". Show that your focus is on the children.
As I wrote about, I suspect that she's made complaints about you even if you didn't come right out and say it. This is a time to know what the priorities are. There are tons of minefields in the legal and child protection aspects.  :)o you have a proactive, experienced lawyer who will stand up and go to bat for you?
Do you both work? If so, then she shouldn't need spousal support. If she doesn't work then your stance, once you get to court is that she should now be looking for a job since it appears the marriage may fail. Your stance should be phrased as looking for her long term future, that is, becoming financially stable on her own two feet. Until then, yes, make sure the rent or mortgage and the utilities get paid and that the car has gas. No, don't pay for a new mink coat, trip to Suntan Beach, or other wasteful spending, well, not unless you are independently wealthy and nothing can make a dent to your financial status.
Do you share joint bank accounts? Beware that she may try to drain them, especially if she's started cases against you with the design to make you look bad when she decides to make the marriage implode. Technically, joint accounts are half yours and half hers. But no one will stop her from taking more than her half. If the joint account is meant to pay the household bills, then decide how to handle it. If there's a lot there and it would be tempting to her to squander or squirrel away, then use the excess there to pay the rent or mortgage a couple months in advance, in other words, get all the bills paid up so that there's less to fight over. If you took the money, saying you would hold it to pay the bills she may then scream. If you pay standard bills early, you're reducing what she might try to squirrel away for herself and her screams will have less impact on others.
Similarly with credit accounts and home equity accounts. Try as best you can to limit what damage the other spouse can do. Same as with bank accounts, the professionals won't prevent her from doing damage since they'll assume it will get worked out in the financials, a later stage of a divorce. However, most of us learned that such things seldom get included as part of the financial division calculations.